Forensic investigations are under way to clarify the cause of the blast, which happened before dawn in the city's Andheri suburb.
"There was a small explosion at a makeshift industrial unit, which caused a slab of wall in an adjacent house in the slum to collapse, killing those who were asleep," a police official in the city control room told AFP, declining to be named.
The injured are being treated at nearby hospitals, he said.
"We came here after hearing people crying for help. We helped an old man escape," eyewitness Sartaj Ahmed told the NDTV news channel, which described the factory as a "chemical producing unit".
"We came out and saw a lot of smoke," said another local resident woken up by the blast.
More than half of Mumbai's residents live in tightly-packed slums in the city.
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41.6% of residents live in slums........mainly muslims and migrants from other cities.....and the area occupied by these slums stands at less than 10% makes it 3 rd most congested in world.....but in size karachi orangi and lyari are far bigger............:)