Smith won his first Academy Award for King Richard but appeared to take offence to a gag Rock made about Pinkett Smith’s short haircut.
She had previously spoken about her struggles with alopecia and said it is what prompted her to shave her head.
Rock said: “Jada, can’t wait for GI Jane 2”, prompting the actress to roll her eyes.
However, Smith walked up on stage and appeared to hit Rock before returning to his seat and shouting twice: “Keep my wife’s name out of your f****** mouth.”
The altercation left Rock shocked and flustered as he tried to resume presenting the best documentary feature category.
The incident cast a cloud over Smith’s acceptance speech for his first ever Oscar, after he was named best actor for his portrayal of Richard Williams, the father of tennis stars Venus and Serena Williams, in King Richard.
Smith apologised to both the Academy and his fellow nominees, but not to Rock, as he collected his gong, joking that he “looks like the crazy father.”
He said: “I want to apologise to the Academy, I want to apologise to all my fellow nominees.
“This is a beautiful moment and I’m not crying for winning an award, it’s not about winning an award for me, it’s about being able to shine a light on all of the people.
“Thank you for this honour, thank you for this moment…I hope the Academy invites me back.”
Following the incident which has made headlines around the world, footage circulated on social media showing Smith dancing to his own songs star-studded after-party.
He celebrated his win at the Vanity Fair afterparty with his wife Jada Pinkett Smith and three children – sons Trey, 29, Jaden, 23, and daughter Willow, 21.
As well as ‘holding court’ according to a Holywood Reporter journalist, the actor was also filmed dancing to his hit ‘Summertime’ and ‘Gettin Jiggy With It’