The incident overshadowed a night which saw Coda, which features a predominantly deaf cast, named best picture, while Troy Kotsur made history as the first deaf male actor to win a gong and Sir Kenneth Branagh won the best original screenplay prize for his semi-autobiographical film Belfast.
Smith, who won his first Academy Award for King Richard, appeared to take offence to a gag Rock made about Pinkett Smith’s short haircut.
The Magic Mike XXL star and Red Table Talk host has previously spoken about her struggles with alopecia and said it is what prompted her to shave her head.
Referring to Pinkett Smith’s buzzcut, 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.”
Breaking down in tears, he said: “Richard Williams was a fierce defender of his family.
“In this time in my life, in this moment, I am overwhelmed by what God is calling me to do and be in this world.”
He added: “I’m being called on in my life to love people and to protect people and to be a river to my people.
“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 have people disrespecting you and you’ve got to smile and pretend like that’s OK.”
He added: “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.”
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.”
After paying tribute to his mother and his family he added: “Thank you for this honour, thank you for this moment…I hope the Academy invites me back.”
The Academy later said that it did not “condone violence of any form”.
A tweet on the official Academy account said: “The Academy does not condone violence of any form.
“Tonight we are delighted to celebrate our 94th Academy Awards winners, who deserve this moment of recognition from their peers and movie lovers around the world.”
The Los Angeles Police Department (LAPD) said no report had yet been filed with the force following the altercation.
“LAPD investigative entities are aware of an incident between two individuals during the Academy Awards programme,” a spokesperson for the force told the PA news agency.
“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.”
Family drama Coda, which stands for child of deaf adults, was named best picture at the ceremony, while Kotsur made history as he was named best supporting actor.
The film also won best adapted screenplay.
Kotsur dedicated his gong to “the deaf community, the Coda community and the disabled community”, adding: “This is our moment”.
West Side Story star Ariana DeBose won the best supporting actress Oscar for her performance as Anita in the classic musical, 60 years after her predecessor in the role, Rita Moreno, earned the statuette herself.
DeBose added: “Now you see why Anita says I want to be in America because even in this weary world that we live in dreams do come true and that’s a heartening thing right now.”
The actress also paid tribute to Moreno, saying she “paved the way for tonnes of Anitas like me”.
Concluding her speech, DeBose added: “Imagine this little girl in the back seat of a white Ford Focus.
“Look into her eyes, you see an openly queer woman of colour, an Afro-Latina, who found her strength in life through art.
“And that’s what we’re here to celebrate.
“So to anyone who has ever questioned your identity or you find yourself living in the grey spaces…I promise you this, there is indeed a place for us.”
Sir Kenneth won the Oscar for his screenplay for Belfast, which is based on his own childhood during the Troubles.
Collecting the statue, he said: “This is an enormous honour for my family and a great tribute to an amazing city and fantastic people.”
He added: “This story is the search for joy and hope in the fact of violence and loss.
“We lost some people along the way.”
He continued: “We miss them, we love them and we will never forget them and we we will never forget all of those lost in the heartbreaking, heart-warming human story of that amazing city of Belfast on the fabulous island of Ireland.
“This means a lot.”
Jessica Chastain was named best actress for The Eyes Of Tammy Faye, while Billie Eilish and her brother Finneas won best original song for No Time To Die from the James Bond film of the same name.
Disney juggernaut Encanto was named best animated film at the ceremony, while Dune, an adaptation of Frank Herbert’s sci-fi novel, won six Oscars, including a best score win for composer Hans Zimmer.