A bomb explosion killed five policemen and eleven policemen had got fragmentation wounds in a suicide attack in the Chechen capital, Grozny.
The attack took place outside a hall where a concert marking Grozny's City Day was about to take place.
A statement from the ministry said police were searching a "suspicious" young man when he detonated a device.
Grozny was ravaged by two wars between Russia and Chechen separatists but has been relatively calm in recent years.
The Russian statement said that police officers on duty at the event "noticed a suspicious young man near metal detectors set up at the concert hall".
"When the police decided to search him and establish his identity, the man blew himself up," it said.
There has been no information about any civilian casualties.
The ministry added that Russian Interior Minister Vladimir Kolokoltsev was preparing to decorate the police involved for preventing what it described as a major terrorist act.
"They gave their lives to save thousands of people who had come to the concert,"
A man who blew himself up in the Chechen capital city of Grozny on Sunday has been identified, a spokesman for the Russian interior ministry told TASS.
“The man has been identified as a resident of the Staropromyslovsky district who has been missing since he left home two months ago,” the spokesman said.
An investigation is underway.
Earlier on Sunday, the press centre of the Russian interior ministry said that that a major terrorist attack had been prevented by the police in Grozny.
“A concert on the occasion of the City Day was planned for Sunday evening in Grozny,” the press centre said.
“Police officers who were on duty at walk-through metal detectors near the concert hall saw a suspicious-looking young man.
When the police officers moved towards him, the man blew himself up.”