The overhead pass connected eastern and western portions of the Andheri railway station, and the incident stranded hundreds of passengers during rush hour.
A witness told India Today TV that he heard shouts of someone at the bridge collapse site calling out to be saved. Another witness said others were trapped.
Aaj Tak television news channel said the bridge was more than 50 years old. Bhakar said incessant rains seemed to have caused cracks in the bridge, resulting in the collapse.
India's Railway Minister, Piyush Goyal, ordered a probe into the incident.
In a tweet, Goyal "directed officials to speed up repair work and rapidly restore traffic in close co-ordination with other departments".
Every day, millions of commuters use the sprawling train network in Mumbai and its suburbs.
Last year, at least 22 people died and 32 others suffered injuries in a stampede triggered by a rumour that a pedestrian overpass had collapsed after concrete chunks fell at another railway station.
- AP