Leading soloist Svetlana Lunkina told a Russian newspaper she had taken leave until the end of the season.
The news that she had left Russia comes in the wake of an acid attack on the company’s artistic director, Sergei Filin, earlier this month.
Svetlana Lunkina alleged the unspecified threats arose from a film project involving her producer husband.
Vladislav Moskalyev was working on a movie about the legendary Russian ballerina Matilda Kshesinskaya but is in dispute with his former business partner, who is reportedly suing him for $3.6 million.
Svetlana Lunkina, 33, who has performed with the Bolshoi since 1997, told the Izvestia publication: “I think we need to react to these threats. These people have no right to interfere in our private lives or my professional work.
“I was supposed to be doing a lot of interesting work, including several premieres.”
She was due to star in a performance of Stravinsky’s The Rite of Spring, choreographed by Britain’s Wayne McGregor, later this year.
Svetlana Lunikna’s allegations are not believed to be related to the assault on Sergei Filin, who had sulphuric acid thrown in this face by a balaclava-clad assailant as he left the Moscow Arts Theatre on January 17.
The attack damaged both of his eyes and he is still receiving treatment for his injuries in a Moscow hospital.
Speaking via video-link this week, Sergei Filin, 42, suggested the assault was carried out by someone looking to “satisfy their ambitions” or “extinguish the pain of resentment”.
“I forgive all those people who were involved,” he went on.
Police are working on the theory that the attack was carried out by someone from within the company.
Svetlana Lunkina told Izvestia she believed it “may not be someone who works at the Bolshoi theatre but someone linked to the theatre and ballet”.
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