The patients were believed to have been convicted of murder but hospitalized because they were found to be legally insane, the Moscow Times reported.
Five other patients who also escaped were later captured, police said.
The nine men, ages 17-20, stormed the nurses' station on their floor around 3 a.m. Friday after a nurse refused to let them watch a soccer match on TV, the Moskovsky Komsomolets newspaper said.
They threatened the nurse on duty with a sharp object and fled with the building's keys, the newspaper reported. They then made their way past fences, a guard and a guard dog before forcing a man and woman out of their car and speeding off.
Neither the police nor the hospital would give further details, citing an ongoing investigation.