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,” ITAR-TASS news agency quoted the ministry as saying.
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