The shootout took place in the morning in the municipality of Tanhuato, in the state of Michoacan, and the death toll was a "preliminary figure," the official said on condition of anonymity.
The official did not provide more details.
Tanhuato is near Yurecuaro, a town where a former vigilante leader who was running for mayor was shot dead during a campaign event last week.
Farmers formed vigilante forces in Michoacan in 2013 to drive out the Knights Templar drug cartel, which has been weakened by arrests of its top leaders.