The gunfight occurred at around 3 p.m. (2100 GMT) near the town of Chilapa, east of the state capital Chilpancingo, state security authorities said in a statement.
A number of guns were recovered from the scene where ten bodies were found in two vehicles damaged by gunfire, the statement said. Two other people were wounded.
The two groups described themselves as community police, the authorities said. It was not clear why they were fighting.
Guerrero, home to the popular beach resort of Acapulco, has long been wracked by some of the worst violence in Mexico.