Dozens of people took shelter on the bridge during a sudden monsoon downpour and the deadly crush started as they emerged all at once, Indian Railways spokesman Anil Saxena said.
Avinash Supe, dean of KEM Hospital, told AFP there were 22 dead.
"There was a huge crowd on the FOB (foot overbridge). Everybody tried to leave at once and it appeared one of them slipped and fell, triggering the stampede," Saxena told reporters.
The bridge connects the Elphinstone and Parel stations in south Mumbai.
The toll is likely to rise further, a disaster management cell spokesman warned. "It was the peak hour rush but the stampede has been brought under control," Tanaji Kamble told AFP.
TV footage showed commuters trying to revive the injured by pumping their chests and also carrying some down stairs to street level.
"We put everybody who was injured in cars, police vans and ambulances and tried to take them to the hospital as quickly as possible," said one witness.
"There were 3-4 women who were badly injured, I don't know whether they survived."
Local trains are the lifeline for the 20 million people of Mumbai. Some 7.5 million commuters take the train daily, with services running every three minutes on average.
Hundreds die every year due to losing their grip on the doors, falling while trying to get into packed compartments, hitting electric poles outside or doing stunts while hanging off the train.
Official figures say some 3,400 people died in 2016 either from falling off the trains or while crossing the tracks of what is the world's most overcrowded suburban rail network.
Stampedes at India's religious festivals are also common with police and volunteer stewards often overwhelmed by the sheer size of the crowds.
In January, six women died in West Bengal state and last year 24 people were killed after a stampede broke out in the Hindu holy town of Varanasi.
