The incident at Elphinstone station, which connects two of the Indian city’s major local lines, was triggered by overcrowding and heavy rain.
The stampede broke out at a narrow footbridge at around 10:30am, when passengers who had taken shelters from the downpour all tried to leave the station at the same time.
Those injured have been taken to nearby hospitals and police are at the scene.
Police officer Niket Kaushik said: “We are still inquiring into the exact reasons.
“It happened on the narrow staircase. All the injured were rushed to the nearest hospitals.
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Pictures from the scene showed people on the ground, with emergency personnel attempting to revive them with water and first aid.
An eyewitness told NDTV: “Two people fell down first. There was heavy rain at that time. Soon, there was a stampede. We took the injured to the hospitals.”
Railway spokesman Anil Saxena told reporters that they would conduct an inquiry into the incident.
He said: “Many were waiting in the rain. There were too many people in a cramped space. When people were trying to rush to their trains, the stampede happened.”
A local resident said the station has been overcrowded and decrepit for years.
The resident added: “It was a disaster waiting to happen”.
Deadly stampedes are fairly common during religious festivals in India, where large crowds gather in small areas with few safety measures.