The attack took place in a Moscow suburb Friday as officers investigated a car crash, RIA Novosti reported.
Investigators say the suspect, who was driving one of the cars, was drunk at the time.
When he was questioned, the man first said a relative gave him the grenade. He said later he found it in the woods, police said.
The relative denied knowing anything about the grenade.
The man has been charged with possession of explosives and attempting to kill police officers.