A Federal Penitentiary Service official said that while walking in the exercise yard, three inmates about to be sent to prisons to serve nine to 25 years, disarmed the guards, put on their uniforms and seized the detention center's library.
"The injured have been hospitalized," the source said, adding that they were probably two top officials at the center.
Earlier, the penitentiary service said no one was hurt when special forces stormed the building.
A law enforcement officer said the three inmates who took the hostages have been detained.
Criminal proceedings have been launched, Moscow's first deputy prosecutor said.