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.”
The Los Angeles Police Department later told Variety that Rock had “declined to file a police report” following the event.