The bridge collapsed at 7.30pm local time (14:00 GMT) as commuters were entering Chhatrapati Shivaji station.
At least 30 people have been injured, according to Indian media.
Images from the scene show rescue workers attempting to move the rubble and treating injured passers-by.
An eyewitness told India’s NDTV: “The whole structure collapsed in front of me. There was debris everywhere.”
The Chief Minister of Maharashtra, Devendra Fadnavis said he was “pained” to hear about the incident. He has ordered a high-level inquiry and announced compensation to the families of those killed.
He added that the injured will also be given compensation and all of their medical costs would be covered.
Sanju Verma, a spokeswoman for governing party BJP, has been criticised on social media for calling the incident a “natural calamity.”
In an interview with local TV station Times Now, Ms Verma denied that a “governance deficit” was behind the accident, instead saying that “a large part of the blame, for want of a better word, was on pedestrians”.
The Chhatrapati Shivaji terminus is a Unesco World Heritage Site.
The incident comes less than a year after a footbridge collapsed in Varanasi, killing at least 18 people. The flyover was still being built when portions of its structure fell on the road being used under it.
In September last year, one person was killed and several others injured when a section of a bridge collapsed in Kolkata.