Friday's gunfight between security forces and an armed gang took place in Tanhuato near the Jalisco state border.
The violence is thought to be drug related and local officials have said that police are among the dead.
The authorities have been fighting a bloody war with the area's most powerful drug cartel, Jalisco New Generation, for years.
It is not clear if the cartel is behind the attack and federal security officials are travelling to the area to investigate.
The town's mayor said a Federal Police convoy had come under fire when it arrived in the area on Friday morning, local radio reported.
Two years ago vigilante groups formed in Michoacan to drive out the Knights Templar drugs cartel. However, last week a former vigilante leader running for mayor in next month's elections was shot dead.
The Jalisco New Generation cartel has increased its presence in the area, with Michoacan and Jalisco becoming among Mexico's most violent states. Gang members are believed to have killed at least 20 police and soldiers since March.
In January, police claimed to have arrested one of the leaders of the the cartel.
Earlier this month several soldiers were killed when a army helicopter was shot down by the cartel.
A further 15 officers were killed in an ambush in April.
At least 39 people have been killed in a shoot-out in the Mexican state of Michoacan.