In February, the producers of the Broadway musical “Natasha, Pierre & the Great Comet of 1812” proudly announced that Okieriete “Oak” Onaodowan, a member of the original “Hamilton” cast, would step into the show’s lead male role after the departure of Josh Groban. But this week, the producers abruptly cut short Mr. Onaodowan’s expected nine-week tenure, saying that during his final three weeks, he would be replaced by a major Broadway star, Mandy Patinkin, who became famous with “The Princess Bride,” won a Tony Award for “Evita,” and is now featured in television’s “Homeland.”

Although producers periodically replace lesser-known performers with big-name actors in the hopes of selling more tickets, the move at “The Great Comet” is prompting outrage among some black actors, who have turned to social media to express their concern that Mr. Onaodowan, who is African-American, was not given sufficient opportunity to succeed before being replaced by a white actor. There are multiple complicating factors. Mr. Onaodowan’s tenure was always going to be short — it just got shorter. Mr. Patinkin is unquestionably better known on Broadway, which could boost publicity for the show and ticket sales during a traditionally slow end-of-summer period. (On Thursday, for example, he was interviewed on NBC’s “Today” show.) And the show is among the most diverse on Broadway, with an African-American actress, Denée Benton, playing Natasha, and multiple other nonwhite actors in the company. But some performers are arguing that the casting change reflects a larger problem in the entertainment business. The move “raises questions about how Black actors are valued and supported within Broadway,” declared the website BroadwayBlack.“It’s like the integration of baseball, where a player has to be twice as good,” Mr. Casal said in a phone interview.

Mr. Onaodowan, who spent months preparing for the role, including learning to play the accordion, did not immediately respond to requests for comment.

The show’s grosses have, to no one’s surprise, dropped since Mr. Groban’s departure. The show had been bringing in about $1.2 million a week with Mr. Groban in the role of Pierre; it brought in $923,571 last week, with Mr. Onaodowan as Pierre. That’s still higher than for most Broadway shows, and still more than the show’s running costs, but not as much as the show is likely to bring in with Mr. Patinkin in the role. Mr. Patinkin is scheduled to play Pierre from Aug. 15 to Sept. 3.

The producers have not said who will play Pierre after Labor Day, but they appear to be considering the occasional use of well-known performers in key roles to excite interest — a strategy many other shows use. This summer, in addition to Mr. Onaodowan, the show has brought in the singer-songwriter Ingrid Michaelson to play a key role (Natasha’s cousin Sonya). The most prominent performer to express concern is the actress Cynthia Erivo, who won a Tony Award last year for her performance in a revival of “The Color Purple.” Ms. Erivo posted a series of seven messages on Twitter on Wednesday, suggesting the changeover was unfair to both Mr. Onaodowan and Mr. Patinkin.

“I honestly am flabbergasted,” she posted. She added, “The disrespect of both actors is highly concerning.”