Sunday night’s Oscar ceremony wasn’t the first time Will Smith’s stardom was defined more by his personal life than by his onscreen roles.

Recently, he has documented his weight loss on a YouTube show, “Best Shape of My Life.” He has appeared on his wife Jada Pinkett Smith’s Facebook show “Red Table Talk” to discuss their marriage briefly falling apart. He tested his personal fortitude in nature adventures around the world in the streaming series “Welcome to Earth” for Walt Disney Co. And last November, he revealed deep secrets in “Will,” a memoir that has spent several months on bestseller lists.

“What you have come to understand as ‘Will Smith,’ the alien-annihilating MC, the bigger-than-life movie star, is largely a construction—a carefully crafted and honed character—designed to protect myself,” he writes in the book.

Still, Mr. Smith, long one of Hollywood’s biggest and most bankable stars, has rarely seemed truly off-script. That is, until Sunday night, when the 53-year-old actor walked onstage during the Academy Awards and struck comedian Chris Rock for making a joke about his wife.  About an hour later, he won the best actor Oscar for his role in “King Richard,” delivering a tearful speech in which he apologized to the Academy and fellow nominees and said: “In this business, you gotta be able to have people disrespecting you and you gotta smile and you gotta pretend like that’s OK.”

What Hollywood, the academy and viewers ultimately make of that night will have ripple effects on the career of one of the planet’s most likable stars.

The Academy of Motion Picture Arts and Sciences said Wednesday that it initiated disciplinary proceedings against Mr. Smith for violating its standards of conduct, “including inappropriate physical contact, abusive or threatening behavior, and compromising the integrity of the Academy.” Mr. Smith will get at least 15 days notice of a vote regarding his violations, and he will be able to offer a written response. Discipline could include suspension, expulsion or other sanctions, the academy said. The board meets again April 18. The academy also clarified that Mr. Smith was asked to leave the ceremony and he refused, adding “we also recognize we could have handled the situation differently.”

Mr. Smith apologized Monday evening to Mr. Rock, the academy and viewers of the show in an Instagram post, calling his behavior “unacceptable and inexcusable.”

“I am embarrassed and my actions were not indicative of the man I want to be,” he said.

How the night will affect Mr. Smith’s career remains unclear. Hollywood has talked of little else since, yet few industry powers will say anything publicly as they await news on the Academy’s next moves. Since the ceremony, some stars have said they found the actor’s actions disturbing.

“Waiting for this sickening feeling to go away from what we all witnessed,” Oscars co-host Amy Schumer said in an Instagram post Tuesday night. Her co-host Wanda Sykes said in an interview with Ellen DeGeneres she was “still a little traumatized.”

Will Smith accepting his Academy Award for best actor.

Photo: Rich Fury/VF22/Getty Images

A representative for Mr. Smith said the actor wasn’t commenting further. A representative for Mr. Rock didn’t respond to a request for comment.

Three in five Americans think Mr. Smith’s actions at the Oscars were wrong, according to a poll of 1,319 people taken on Monday by the research company YouGov.

Mr. Smith is one of the few actors in contemporary Hollywood who can largely control his own destiny by greenlighting projects on star power alone, and often coming on board as a producer.

He has several high-profile projects in development, most notably an Apple Inc. movie called “Emancipation” scheduled for release later this year that could put Mr. Smith back on the awards circuit in months.

Will Smith and Tommy Lee Jones starring in the blockbuster “Men in Black.”

Photo: Columbia Pictures/Everett Collection

Apple hasn’t made any changes to its plan for a late 2022 release, according to a person familiar with the matter.

The production of “Emancipation” reflects Mr. Smith’s signature star power. When he agreed to star in the film in 2020, the project became one of the buzziest titles at a virtual market held by the Cannes Film Festival. Mr. Smith stars in the true story of a runaway slave who escaped to the North and helped spark anti-slavery campaigns when photos of his lash-scarred back were published.

Bidders swooped in for the chance to work on the movie. Apple ended up coming on board to produce the film for more than $100 million, according to a person familiar with the matter.

Apple bought the project with plans to release it in theaters and on its AppleTV+ streaming service, a rollout similar to its 2021 release of “CODA,” which won best picture on Sunday about an hour after Mr. Smith’s slap.

Mr. Smith started his career mining his personal story, as a Philadelphia-raised rapper and star of “The Fresh Prince of Bel-Air,” a comedy series recently remade as a drama. His film career reached stratospheric heights with “Independence Day,” the 1996 blockbuster in which he played a pilot fending off a global alien invasion.

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The movie was the highest-grossing release that year—it made $553 million in the U.S. when grosses are adjusted for inflation—and established a template for the studio-driven “event movie,” complete with Super Bowl ads, Time magazine covers and tie-in toys. Soon Mr. Smith ruled the July 4 weekend, when “Men in Black” followed in 1997.

Mr. Smith started producing some of his own projects in the early 2000s, and in 2019 he founded Westbrook, a media company that focused on his entire family’s entertainment pursuits. In January, the private-equity-backed Candle Media paid $60 million for more than 10% of Westbrook Inc., continuing a string of Wall Street investments in celebrity-oriented media ventures.

The formation of Westbrook illustrated how Mr. Smith’s celebrity is, increasingly, a package deal: his wife, Ms. Pinkett Smith, and their two children, Jaden and Willow. Soon the interpersonal relationships of the four were fodder for programming.

Will Smith in Red Table Talk.

Photo: Facebook Watch

Mr. Smith and his family have lately embraced the same kind of confessional entertainment that helped deliver celebrity families like the Kardashians. Mr. Smith’s children with Ms. Pinkett Smith, as well as Trey, a child from a previous relationship, have all played themselves on TV.

In July 2020, Mr. Smith appeared on his wife’s talk show to discuss rumors of infidelity in the relationship. The incident concerned a separation the couple went through about four years prior.

“I was done with you,” said Mr. Smith. “Marriages have that, though.”

During that separation, Ms. Pinkett Smith said she got into “a different kind of entanglement” with another man. The couple’s 13-minute conversation is heavy in the language of therapy, including details of Ms. Pinkett Smith’s co-dependency and childhood trauma.

In his book, Mr. Smith refers to past plans for his family’s “world domination.” Yet, in “Best Shape of My Life,” he expresses concern about the constant spotlight.

“It’s too much,” he says. “I just think it’s not people’s business.”

—John Jurgensen contributed to this article.

Write to Erich Schwartzel at erich.schwartzel@wsj.com and Ellen Gamerman at ellen.gamerman@wsj.com