Prosecutors said on April 5 there was evidence suggesting the man, who is now in a coma, was beaten by two other detainees who were later freed by police.
The beating victim was found unconscious in the street.
Prosecutors say they are probing whether police attempted to cover up the March 30 incident.
On April 4, it was announced that three Moscow police were expected to face trial for allegedly using a gas mask to torture a female murder suspect last year.
The woman survived.
Russian police have been facing increased scrutiny after the death of a man in custody in Kazan last month.