In his Instagram post, Smith added he "would like to publicly apologize" to Rock, adding that the slap was "out of line" and "wrong."
"I am embarrassed and my actions were not indicative of the man I want to be," he continued. "There is no place for violence in a world of love and kindness."
The actor also apologized to the Academy, the Oscars producers, everyone in attendance and everyone watching from home.
"I would like to apologize to the Williams Family and my King Richard Family," he added. "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."
At first, Smith seemingly laughed at the joke, but then got up and hit Rock in the face as he stood on the stage. Rock appeared to be in shock, and Smith sat back down and shouted, "keep my wife's name out of your (expletive) mouth," twice.
The feed from ABC appeared to cut off for many viewers during the incident, but international broadcasts picked up the entire moment, with Rock saying, "Will Smith just smacked the (expletive) out of me."
During his acceptance speech for best actor later in the night, Smith apologized to the Academy, but not to Rock.
"I'm being called on in my life to love people and to protect people and to be a river to my people," he said through tears. "I know to do what we do, you’ve got to be able to take abuse, you’ve got to be able to have people talk crazy about you. In this business you’ve got to be able to have people disrespecting you. And you gotta smile and you've got to pretend like that’s okay."
He continued: "Art imitates life. I look like the crazy father, just like they said about Richard Williams. But love will make you do crazy things."
Since the broadcast, the Academy has launched an investigation into the incident, and social media has been abuzz with reactions to the controversial moment. Rock declined to file a police report Sunday, Los Angeles police appeared to confirm.
On Sunday, the Academy released a statement saying the organization does not condone violence. And the real Richard Williams, whom Smith won an Oscar for portraying, told NBC News via his son Chavoita LeSane that the Williams family does not "condone anyone hitting anyone else unless it’s in self-defense."