The helicopter was carrying out an operation in the Apatzingan region that has difficult land access, tweeted Silvano Aureoles, the governor of Michoacan.
The operation was focused on apprehending leaders of criminal cells, CNN quoted the governor as saying.
It was not immediately clear how the helicopter was downed.
Michoacan has long been a flash point in Mexico’s drug war, and battles between criminals and security forces occur.
In May 2015, a shootout left 42 gunmen and one federal police officer dead, CNN added.