In its report, the Izvestia daily cited Svetlana Lunkina as receiving threats and facing blackmail.
"We need to react to these threats," Lunkina told Izvestia.
"These people have no right to interfere in our private lives or my professional work."
She did not elaborate exactly on the nature of the threats.
The Izvetia report comes after an acid attack on the Bolshoi's chief last week that left his face burned.
The prima ballerina, 33, who has been in Canada for the last six months, registered a dance studio last October in Kleinberg, Ont., just north of Toronto, and will be teaching at a city studio for a month starting Friday.
Kevin Pugh, artistic director with Dance Teq, said he met Lunkina when she came to the studio to take classes last fall.
"When I was in the hospital, she subbed for me once, and people loved her," Pugh told The Canadian Press.
"I just had to wait to see if she had her papers."
Pugh, a former dancer with the National Ballet of Canada, said Lunkina is a permanent resident and has her work permit.
He said he doesn't know her that well yet, but said she seemed "a little nervous" about giving out her contact details.
The Bolshoi Theatre is one of Russia's premier cultural institutions. It is best known for "Swan Lake" and the other grand classical ballets that grace its Moscow stage.
But backstage, the ballet company has been troubled by deep intrigue and infighting that have led to the departure of several artistic directors over the last few years.
Earlier this month, someone splashed artistic director Sergei Filin with acid.
Lunkina, who has danced with the Bolshoi since 1997, said there is no apparent connection between the threats against her and the acid attack.
She did say, according to Izvestia, the threats she has received are linked to a film her husband, producer Vladislav Moskalev, had been working on until he got into a dispute with his business partner.
Moskalev is listed as the director of Lunkina's Canadian-registered dance company.
Lunkina danced in Toronto in a Canadian Ballet Theatre production of Giselle in 2007.
She was due to take a starring role in a new version of the "Rite of Spring" at the Bolshoi this year.
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