LOS ANGELES - It has been called “the slap heard around the world.”

But it also may be the smack—televised worldwide at Sunday night’s Academy Awards show—that gets popular actor Will Smith sanctioned, despite an apology he issued Monday evening saying he was “out of line.”

The Academy of Motion Pictures Arts and Sciences on Monday condemned the actions of Mr. Smith during Sunday night’s Oscars presen- tation and launched an inquiry into his slapping of comedian and presenter Chris Rock during the show.

In a statement Monday, the film academy said: “The Academy condemns the actions of Mr. Smith at last night’s show. We have officially started a formal review around the incident and will explore further action and consequences in accordance with our bylaws, standards of conduct and California law.”

The fallout from Mr. Smith’s onstage assault continued Monday, as Hollywood and the public continued to wrestle with a moment that stunned the Dolby Theatre crowd and viewers at home, and may have passed all others — even that gold-standard flub, EnvelopeGate — in Academy Awards infamy.

Mr. Smith stunned the Dolby Theatre crowd and viewers at home when he took to the stage during Mr. Rock’s remarks after the comedian made a joke about Mr. Smith’s wife, Jada Pinkett Smith. Mr. Rock said, “Jada, I love you. ‘G.I. Jane 2,’ can’t wait to see it.”

The joke touched a nerve. Ms. Pinkett Smith, whose head is shaved, has spoken publicly about her alopecia diagnosis.

Mr. Smith strode on stage and slapped Mr. Rock across the face. Back in his seat, Mr. Smith twice shouted for Mr. Rock to “keep my wife’s name out your (expletive) mouth.” His words echoed clearly throughout the Dolby Theatre, though ABC television cut the audio for about 15 seconds.

Within an hour, Mr. Smith won the Academy Award for best actor for his role as Richard Williams, the father of tennis phenoms Venus and Serena Williams, in the film “King Richard.”

During his teary acceptance speech, Mr. Smith apologized, but only to the academy and to his fellow nominees.

On Monday, he issued a stronger apology — specifically mentioning Mr. Rock—in a statement released by his publicist and posted on Instagram:

“Violence in all its forms is poisonous and destructive. My behavior at last night’s Academy Awards was unacceptable and inexcusable. Jokes at my expense are part of the job, but a joke about Jada’s medical condition was too much for me to bear and I reacted emotionally.

“I would like to publicly apologize to you, Chris. I was out of line and I was wrong. I am embarrassed and my actions were not indicative of the man I want to be. There is no place for violence in a world of love and kindness.

“I would also like to apologize to the Academy, the producers of the show, all the attendees and everyone watching around the world. I would like to apologize to the Williams Family and my King Richard Family. I deeply regret that my behavior has stained what has been an otherwise gorgeous journey for all of us.

“I am a work in progress.

“Sincerely,

“Will”

Ms. Pinkett Smith responded Tuesday with a graphic on Instagram that read: “This is a season of healing and I’m here for it.” She offered no further comment.

After the show Sunday night, the academy posted a statement condemning violence and called a board of governors meeting Monday to discuss the incident.

The Los Angeles Police Department said Sunday it was aware of the incident but was not pursuing an investigation because the person involved declined to file a police report.

Some academy members, including writer-producer Marshall Herskovitz, called for the academy to take disciplinary action against Mr. Smith.

“He disgraced our entire community tonight,” Mr. Herskovitz wrote on Twitter.

Whoopi Goldberg, a member of the Academy’s board of governors, said Monday on her show, “The View,” “We’re not going to take that Oscar from him. There will be consequences, I’m sure.”

A sense of disbelief hung in the air at the Dolby Theatre after Mr. Smith’s assault, and it didn’t dissipate Monday. Not only was it a hard-to-fathom break with decorum on live national television — an incident so dramatic, even movie-like, that many initially assumed it was a staged bit — it seemed wildly out of character for one of Hollywood’s most relentlessly upbeat stars.

All of this less than an hour before Mr. Smith reached possibly the climactic moment of his career, winning his first Oscar, for best actor for “King Richard.”

“In a way, I feel bad for Will Smith, too, because I think he let his emotions get the bet- ter of him, and this should have been one of the great nights of his life,” said former Oscar host Jimmy Kimmel on Bill Simmons’ podcast. “And now it’s not. Was there anyone who didn’t like Will Smith an hour ago in the world? Like no one, right? Now he doesn’t have a single comedian friend — that’s for sure.”

Some questioned whether Mr. Smith should have been allowed to continue to sit front and center after smacking Mr. Rock. Several stars rushed to counsel and calm Mr. Smith, including Denzel Washington, Tyler Perry and Bradley Cooper. But the timing also was awkward because the best actor category was due up soon after, and Mr. Smith had long been considered a lock for the award.

“I know we’re all still processing, but the way casual violence was normalized tonight by a col- lective national audience will have consequences that we can’t even fathom in the moment,” wrote Janai Nelson, president and director-counsel of the NAACP Legal Defense Fund, on Twitter.

The joke that provoked Mr. Smith was not part of Mr. Rock’s routine during the rehearsals leading up to the show, according to two sources close to production who were not authorized to speak publicly.

The show’s producer, Will Packer, was criticized as being too flippant for posting a tweet Sunday that read: “Welp ... I said it wouldn’t be boring #Oscars.” But Mr. Packer took to social media again Monday following overwhelming public criticism for Mr. Smith, in part, for wrecking a show produced by a Black man.

“Black people have a defiant spirit of laughter when it comes to dealing with pain because there has been so much of it.

I don’t feel the need to elucidate that for you,” Mr. Packer tweeted. “But also don’t mind being transparent and say (sic) that this was a very painful moment for me. On many levels.”

Mr. Rock had joked about Ms. Pinkett Smith before. He hosted the 2016 Oscars, when some were boycotting the ceremony over the #Os- carsSoWhite group of nominees, including the Smiths. Said Mr. Rock: “Jada boycotting the Oscars is like me boycotting Rihanna’s panties. I wasn’t invited.”

In the press room backstage on Sunday, where winners take a few questions from the media, the academy tried to stifle questions about the incident, at one point stopping actress Jessica Chastain, who won an Oscar for best actress for her role in “The Eyes of Tammy Faye,” from talking about it.

But that didn’t prevent the moment from over- whelming talk at the Oscar after-parties and beyond. Some came to Mr. Smith’s defense, including actress-comedian Tiffany Haddish, who co-starred with Ms. Pinkett Smith in “Girls Trip.”

“Maybe the world might not like how it went down, but for me, it was the most beautiful thing I’ve ever seen because it made me believe that there are still men out there that love and care about their women, their wives,” Ms. Haddish told People magazine.

Mr. Smith, meanwhile, merrily posed for photographs Sunday night with his family outside the Vanity Fair party. Inside, cell phone videos captured him dancing to “Gettin’ Jiggy Wit It” while clutching his Oscar. Their son, Jaden, tweeted: “And That’s How We Do It.” On Instagram, Mr. Smith posted: “Me ’n Jada Pinkett Smith got all dressed up to choose chaos.”

The drama overshadowed some historical wins at an Oscars. The deaf family drama “CODA” became the first film with a largely deaf cast to win the Academy Award for best picture. For the first time, a streaming service, Apple TV+, took Hollywood’s top honor, signaling a profound shift in Hollywood and in moviegoing. Ariana DeBose of “West Side Story” became the first Afro-Latina and the first openly LGBTQ actor to win best supporting actress.

Musician Questlove also won the best documentary feature Oscar for “Summer of Soul,” which he directed, about the 1969 Harlem Cultural Festival known as the Black Woodstock.

And actor Samuel L. Jackson, 73, received an honorary Academy Award for lifetime achieve- ment at the Governors Awards in a non-televised ceremony last Friday. It was presented by actor Denzel Washington, who was nominated for best actor—the same category as Mr. Smith – for his role in “The Tragedy of MacBeth.”

As stunning as Mr. Smith’s slap was, it wasn’t shocking that such a pivotal moment in the actor’s life would play out in the public eye. Particularly in recent years, Mr. Smith has been among the most candid of stars, publicly acknowledging last year that he and Ms. Pinkett Smith have an “open marriage.”

While Ms. Pinkett Smith’s Facebook series “Red Table Talk” has been a platform for airing family drama, Mr. Smith has chronicled his own journey in the YouTube series “The Best Shape in My Life,” which included one episode documenting Mr. Smith discussing his regrets as a parent with his children.

Mr. Smith also penned, with personal-growth author Mark Manson, the memoir “Will,” published earlier this year. It rocketed upAmazon sales rankings Monday to No. 32. In it, he described how he was molded by his loving but hard-drinking and militaristic father. In one chapter, he recalls as a 9-year-old seeing him hit his mother. Guilt at not protecting his mother, Mr. Smith wrote, left him with complicated feelings that he connects with fueling his own rise in show business. When his father was elderly and confined to a wheelchair, Mr. Smith confessed feeling an impulse to push him down a staircase.

“My personal journey into the depths of the joys and traumas of my past are definitely helping me to expand and build out a greater emotional toolbox that will allow me to portray more complex characters,” Mr. Smith said last fall in an interview with The Associated Press.

For Mr. Smith, playing Richard Williams in “King Richard” brought together all of these deep-rooted emotions — and it won him the Oscar. It also might have compelled his actions on Sunday.

“Art imitates life,” Mr. Smith said in accepting the award. “I look like the crazy father, just like they said about Richard Williams.”