Will Smith slapped Chris Rock in the face on stage at the Oscars after the comic made a joke about the actor's wife Jada Pinkett Smith.
"Jada, can't wait for GI Jane 2," Rock said, in an apparent reference to her shaved hairdo - a result of the hair loss condition alopecia.
Smith walked on stage and struck Rock before returning to his seat and shouting: "Keep my wife's name out of your [expletive] mouth."
He later apologised to the Academy.
In a tearful acceptance speech for best actor, he also said he wanted to apologise to all his fellow nominees. There was no specific apology for Rock.
The star picked up the first Oscar of his career for playing the father of tennis legends Venus and Serena Williams in King Richard.
"Art imitates life," he said. "I look like the crazy father, just like they said about Richard Williams. But love will make you do crazy things."
The Academy of Motion Picture Arts and Sciences, which organises the Oscars, tweeted that it "does not condone violence of any form".
Rock's joke referred to 1997 film GI Jane, in which Demi Moore played the title role with a severe buzzcut.
Pinkett Smith rolled her eyes at the comment, while Smith appeared to initially laugh and clap his hands before he was seen on stage, walking up to Rock.
The comedian looked stunned in the immediate aftermath of the incident, but told the audience: "That was the greatest night in the history of television."
He is yet to comment further on what happened.
The Los Angeles Police Department later told Variety that Rock had "declined to file a police report" following the event.
After the incident, Rock handed over the best documentary prize, which was the reason he was on stage.
According to The Hollywood Reporter's Scott Feinberg, a tearful Smith needed to be "pulled aside and comforted" by Denzel Washington and Tyler Perry.
The trio could be seen talking just in front of the stage during an advert break, with Washington and Perry putting their hands on his shoulders. A Star is Born actor Bradley Cooper was also seen standing with Smith and appearing to reassure him.
Presenting the next section, Sean "Diddy" Combs said: "Will and Chris, we're going to solve that like family. Right now we're moving on with love."
Fresh Prince of Bel Air actor Smith later wrote on Instagram: "You can't invite people from Philly or Baltimore nowhere!!" - referring to his birthplace Philadelphia, Pennsylvania, and Baltimore, Maryland, where his wife of 24 years is from.
Smith attended the Vanity Fair Oscar party with sons Trey and Jaden, daughter Willow and his wife - smiling for photographers and posing with his award on the red carpet.
Other guests at the party reacted to the incident, with filmmaker David Furnish saying he tells his sons with Elton John "don't hit anybody... under any circumstance".
But actress and comedian Tiffany Haddish defended Smith, saying he had been standing up for his wife.
Jaden Smith tweeted after his father hit Rock: "And that's how we do it."
Other members of the film industry criticised Smith, with The Last Samurai producer Marshall Herskovitz calling on the Academy to take disciplinary action against him and Star Wars actor Mark Hamill calling it "the ugliest Oscar moment ever".
He added: "Stand-up comics are very adept at handling hecklers. Violent physical assault... not so much."
Comedian and actress Kathy Griffin said she now feared for the safety of comedy performers.
"Let me tell you something, it's a very bad practice to walk up on stage and physically assault a comedian," she said. "Now we all have to worry about who wants to be the Will Smith in comedy clubs and theatres."
By Steven McIntosh, entertainment reporter at the Oscars
Here in the Dolby Theatre in Los Angeles, there was a shocked reaction from journalists.
Reporters had been taking part in the traditional backstage press conference, but attention suddenly turned to the overhead screens and what was going on at the ceremony.
At first, it had seemed like some kind of set-up. Smith even appeared to laugh at first after Rock delivered his line about his wife looking like GI Jane.
Jada looked annoyed, but at this point it was still assumed this was all part of some kind of pre-planned routine.
Doubt began to creep in when Smith rose from his seat and hit Rock on the stage. Of course, these guys are veterans of film and television, and would know how to carry out a fake stage slap. Except, everyone was starting to think, it didn't look that fake.
By the time Smith was sitting back in his seat and shouting to Rock to "keep my wife's name out your [expletive] mouth", it was clear this was no sketch. A professional like Smith would know better than to drop the F-bomb on stage during a live TV broadcast.
Much like previous Oscars that were defined by their viral moments - such as Ellen's group selfie or the best picture winner mix-up in 2017 - this will now forever be the Oscars where Will Smith punched Chris Rock.
Pinkett Smith first talked about her hair loss struggle in an episode of her Facebook chat show, Red Table Talk, back in 2018.
She said: "I've been having issues with hair loss. And it was terrifying when it first started."
The Girls Trip star said she first suspected she had alopecia after "handfuls of hair" came loose in the shower.
"I was just like, 'Oh my God, am I going bald?' It was one of those times in my life where I was literally shaking with fear," she explained. "That's why I cut my hair and continue to cut it."
It was not the first time Rock has made a joke about Pinkett Smith at the Academy Awards. He hosted the 2016 event, when she was among the stars who boycotted the ceremony due to a lack of diversity in the nominations.
That year, he said: "Jada Pinkett Smith boycotting the Oscars is like me boycotting Rihanna's panties - I wasn't invited!"
Other winners at Sunday's ceremony included Jessica Chastain, who picked up best actress for The Eyes of Tammy Faye; Jane Campion, who won best director for The Power of the Dog; and Apple TV film Coda, which was named best picture.
Best supporting actress went to Ariana DeBose for West Side Story, while Troy Kotsur won best supporting actor for Coda, which also picked up best adapted screenplay.
Sci-fi epic Dune won six awards in total including technical categories for best visual effects and best cinematography.
Will Smith's best actor acceptance speech
Smith took to the stage twice during the Oscars ceremony - once to take issue with what Rock had said about his wife, and then less than an hour later, to accept his first Academy Award.
Accepting the Oscar for best actor for King Richard, he said Richard Williams was a "fierce defender of his family" and that he himself was "being called on" in his life "to love people and to protect people".
He ended it saying he hoped the Academy would invite him back.