In a statement Monday, the film academy said it will also "explore further action and consequences in accordance with our Bylaws, Standards of Conduct and California law."
Smith stunned the Dolby Theatre crowd and viewers at home when he took the stage during Rock's remarks after the comedian made a joke about Jada Pinkett Smith, Smith's wife. Rock turned to Jada Pinkett Smith, Smith's wife, and said, "Jada, I love you. 'G.I. Jane 2,' can't wait to see it."
WATCH: Will Smith's shocking Oscars stage confrontation with Chris Rock
The joke touched a nerve. Pinkett Smith, whose head is shaved, has spoken publicly about her alopecia diagnosis. Rock has also previously joked about her. Rock hosted the 2016 Oscars, when some were boycotting the ceremony over the #OscarsSoWhite group of nominees, including the Smiths. Said Rock: "Jada boycotting the Oscars is like me boycotting Rihanna's panties. I wasn't invited."
Smith strode on stage and slapped Rock across the face. Back in his seat, Smith twice shouted for Rock to "get my wife's name out your (expletive) mouth." His words echoed clearly throughout the Dolby, though ABC cut the audio for about 15 seconds. Within an hour, Smith won best actor. During his acceptance speech, Smith apologized to the academy.
"The Pursuit of Happyness" star appeared remorseful when he returned to the stage shortly after, to accept the Oscar for best actor for his role as Richard Williams, the father of Venus and Serena Williams, in the film "King Richard."
During his emotional speech, Smith apologized to the Academy and his fellow nominees for the incident but did not mention Rock by name.
Smith posted a statement on Instagram Monday afternoon about the incident, issuing a public apology to Rock for the first time.
"I would like to publicly apologize to you, Chris," Smith wrote. "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."
Earlier Monday, the LAPD announced that Chris Rock will not be pressing charges and had not filed a police report.
"LAPD investigative entities are aware of an incident between two individuals during the Academy Awards program," the department told CNN in a statement. "The incident involved one individual slapping another. The individual involved has declined to file a police report. If the involved party desires a police report at a later date, LAPD will be available to complete an investigative report."
After the show Sunday night, the academy posted a statement condemning violence. Some academy members, like writer-producer Marshall Herskovitz, called for the academy to take disciplinary action against Smith.
"He disgraced our entire community tonight," wrote Herskovitz on Twitter.
MORE: Oscars drama shines light on Jada Pinkett Smith's alopecia, condition that causes hair loss
That single action on what was one of the biggest nights of Smith's career instead shined a light on the actor for all the wrong reasons
"If the Academy were my client, one of the things I'd be saying to them right now is they must hold Mr. Smith accountable for his actions," crisis PR expert Mike Paul, aka The Reputation Doctor," said.
He says what unfolded goes way beyond Smith and Rock, involving dozens on stakeholders with ties to the awards show -- the biggest of which is the Academy itself.
"They don't want that precedent to be set, and they want to make sure it's not coming back on the Academy as being part of the problem," he said.
He believes doing nothing is not an option, and as Smith is a multi million dollar brand, his projects may now take a hit.
"If there's a morality clause that's there, they could have action on him," Paul said. "They could say your value was a 10, now it's a 6 or 5 after the slap."
WATCH: Will Smith's full acceptance speech
Whoopi Goldberg, a member of the Academy's board of governors, said Monday on "The View": "We're not going to take that Oscar from him. There will be consequences, I'm sure."
While Smith's actions have been widely condemned on social media, with many arguing he should be charged with assault, his 23-year-old son, Jaden Smith, shared a tweet shortly after the incident, which said: "And That's How We Do It."
CNN has contacted Rock's representatives for further comment.
Smith appeared to predict the mayhem of Oscars night in an Instagram post hours earlier. Sharing a video of himself and his wife in their red carpet attire with his 60 million followers, he wrote: "Me 'n @jadapinkettsmith got all dressed up to choose chaos."
(The Associated Press and CNN contributed to this report)