Almost all of the dead are suspected criminals, said the official - speaking anonymously, but several police officers are also thought to have been killed.
The gunmen took cover in a nearby ranch during the battle with police.
The circumstances leading to the violence are not yet clear and federal security officials are travelling to the area to investigate.
The town's mayor told local radio 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.
