Two men were arrested and two other suspects were being sought, The Detroit News reported.
Capt. Monica Yesh of the Metro South Post said the trooper suffered a leg wound and was reported in serious condition. His name was not released but he was described as a 12-year veteran of the state police.
Lt. Mike Shaw of the Metro North Post said officers stopped a car about 3:50 a.m. that matched the description of a vehicle used in a series of armed robberies.
Four men ran from the car and police caught two of them before the shootout occurred at a nearby home, the News said.
Police surrounded and later stormed the building but no one was inside, the report said.