There were no passengers in the coaches at the time. Images showed one of the coaches completely destroyed in the fire.
Officials suspect a short-circuit might have caused it.
Mumbai has a 9 km railway corridor for the monorail from Wadala to Chembur.
Earlier this year, in a near miss involving the monorail, two trains in opposite directions nearly collided head-on after ending up on the same track near Chembur. The trains were stopped before a disaster could take place.