The attack happened late on Thursday as Sergei Filin, an award-winning ballet star, was walking home in central Moscow.
Doctors are now fighting to save his eyesight and Interfax news agency says he will be sent to a clinic abroad.
A Bolshoi spokesman said Sergei Filin, 42, had suffered months of threats.
According to local media, it is suspected that he was the victim of infighting and rows between different groups of dancers at the Bolshoi.
According to the Bolshoi statement, the assailant shouted to Sergei Filin as he was approaching the entrance to his apartment block, then threw acid in Filin’s face.
Sergei Filin then got help from a warden keeping watch over nearby cars.
The theatre’s executive director, Anatoly Iksanov, told Russian television that Sergei Filin was “uncompromising” in his management style.
“If he thought a performer was unready to play a certain role, or incapable of it, he would not let the performer do it,” he said.
Tensions at the Bolshoi over its artistic programme have been widely reported in Russian media.
In 2011 two ballet stars – Natalia Osipova and Ivan Vasiliev – resigned in protest at the Bolshoi’s new repertoire.
At the time of Sergei Filin’s appointment the head of the Bolshoi’s ballet troupe, Gennady Yanin, resigned after erotic photographs purporting to be him were posted on a website.
Another celebrated performer, Nikolai Tsiskaridze, sharply criticized Sergei Filin in early 2012.
Sergei Filin:
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