A special operation to detain the militant began at about 2:00 p.m. Moscow time (11:00 a.m. GMT) Sunday in the village of Ordzhonikidzevskaya, the ministry said.
"Upon an attempt to enter a private home, an automatic fire was opened at the police. The home was sealed off and an exchange of fire followed," said Nazir Yevloyev, the ministry's spokesman.
"The militant ignored the calls to surrender and blew up himself and a woman," Yevloyev said.
The dead militant's identity has been established while the woman who was in the home together him is being identified, a source in the republican law-enforcement bodies said.
The police found two Makarov pistols, one of them with a silencer, and a large amount of ammunition at the scene, the press secretary said.