The ministry said officers stopped a suspicious man on a street in Grozny on Thursday night to check his documents and that the man opened fire with a pistol and then fled to a nearby apartment.
Police surrounded the apartment building and in the subsequent shooting, two officers and the suspect were killed, the ministry said.
It later identified the man as a high-placed comrade of Doku Umarov, the leader of Chechnya's separatist rebels.
Also Thursday, a group of about 30 camouflage-clad gunmen set afire the houses of two police officers and the local administration building in the Chechen village of Yandi, the ministry said.
Chechen separatists have fought two wars with Russian forces since 1994. Large-scale fighting faded away early in the decade, but small attacks on police and military patrols continue. Russian forces have apparently strong control of the republic's northern flatlands, but have been unable to drive them out of the mountainous southern sector or purge them from the capital.
Russia's Ambassador to Belarus, Mikhail Babich, said that Moscow would treat any military intervention in the affairs of Belarus as an attack on Russia
The month of October was rich with rare astronomical phenomena.