Two police officers were among those killed in the shootout on Tuesday involving members of the powerful Knights Templar gang, which controls large parts of Michoacan.
The fighting broke out after gang members set up roadblocks in the villages of Puerto El Mamey and El Carrizo, the ministry said.
In May, Mexican President Enrique Pena Nieto sent a general to take charge of police and military operations in the state.
Earlier on Tuesday, Mexican officials said six people believed to be members of rival drug cartels were killed in a gunbattle in northern Mexico.
It took place in the town of Mesa de la Reforma, in Chihuahua state.
Chihuahua has seen some of the worst violence between rival drug cartels and Mexican security forces.
Security experts have warned of an escalation of the violence after the recent arrests of the reputed boss of Los Zetas cartel, Miguel Angel Trevino Morales, and Víctor Hugo Delgado Renteria, allegedly one of the heads of the Jalisco Nueva Generacion cartel.
Voice of Russia, dpa