Investigators questioned Mr. Filin on Saturday, and the police have said they are investigating a variety of theories, including professional grudges or disputes over money. His associates and relatives have speculated that Mr. Filin had threatened commercial interests associated with the theater, or that one of his rivals hoped to take his job. Yuri Burlak, one of his predecessors in the position, told the newspaper Izvestiya that he favored the second theory, noting that Mr. Filin had three years left on his contract.

Nikolai Tsiskaridze, a popular principal dancer who has clashed publicly with Mr. Filin, condemned the crime on Russia’s Channel One news on Sunday, saying it went leagues beyond the artistic rivalries that are woven into the theater’s history.

“There have always been stories about glass in point shoes, about cats thrown onto the stage, about brooms thrown onto the stage and so on,” he said. “This is a peculiar part of theatrical life, and no one has changed it,” he said. “That is just hooliganism compared to what happened to Sergei, because throwing acid in someone’s face — that is a monstrous crime, which does not just disfigure a person’s life, but strips him of livelihood, of his eyesight itself. This is monstrous.”

Mr. Filin has made clear his intent to stay on as the ballet company’s artistic director, focusing on his creative plans during a Saturday conversation with Russia’s minister of culture, and the theater’s director said there were no plans to replace him.