Rescue work was ongoing at the site in the financial capital as local police said they feared five or six people still lay trapped under the rubble.
"We received five patients from the site of the collapsed building," said a duty officer at JJ Hospital in Mumbai, one of two hospitals where the injured were taken.
"Two of them were brought in dead and the other three are critical with severe head and fracture injuries."
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Local media reports said the building housed a beer bar and a factory.
A senior police official in the city gave a lower death toll, saying one person had been killed and at least five injured, but said rescue work was still ongoing.
"We are trying to ascertain if five or six people are actually trapped under the rubble," Dhananjay Kulkarni, a spokesman for Mumbai Police told AFP, adding that the cause of the collapse was not known.
Mumbai has been hit by several deadly building collapses in recent years, often caused by shoddy construction, poor quality materials or ageing buildings.
But in one of India's most crowded and expensive cities, people still use old, dilapidated buildings because of a shortage of space.
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