The burglars broke into Volochkova's Moscow private house around 6:30 a.m. and beat a woman, her husband and another woman, all servants of the former Bolshoi Ballet prima ballerina, before taking the safes and fleeing.
Volochkova, 37, was not home but her 8-year-old daughter Ariadna was, a police source told RIA Novisti.
Police did not immediately report what was in the safes or the value of the stolen property.
"Yes. My house has been robbed. But one cannot rob my soul! It is too rich!" Volochkova posted on her Twitter account.
"Oh, God. How much anger you have... People... Save your souls," she said.
The dancer, who now has a solo career, including ice dancing, and is a TV and movie actress, said on Twitter she was "afraid to go back home."
"During Holy Week to commit such a sin! Burn them in hell," she said in another Twitter message.