Many others are feared trapped beneath the three-storey building in Thane after the incident early on Tuesday.
Reports say the municipality had declared the old, dilapidated property dangerous to live in, but residents had refused to vacate.
More than 100 people have died in residential building collapse s in Mumbai in the last two years.
Rescuers are searching through the rubble for survivors after the building in the Naupada area collapsed while families were sleeping inside, an official said.
"Eleven bodies have been recovered and seven people pulled out alive. Another one person is missing," rescue official Alok Avasthy told the AFP news agency.
He said people were living in the 50-year-old building even though it "had been declared unsafe by the government two years ago".
"We pulled a family of five to safety with the help of a sniffer dog who tells us that there is still some life in there," Mr Avasthy said.
Tuesday's incident comes a week after nine people were killed when another three-storey building collapse d during heavy monsoon rains in Thakruli, a Mumbai suburb.
Property prices and rent in Mumbai are among the highest in Asia. Many citizens are forced to live in old, dilapidated properties in a land-scarce city where an estimated 60% of its 18 million people live in slums and shantytowns.
There are more than 14,000 buildings in Mumbai that are more than 70 years old.
Between 2008 and 2012, there were 100 building collapse s in which 53 people died and 103 others were injured, authorities say.
Poor construction material and building practices are often blamed for many of the building collapse s in India.
Last year an 11-storey building in southern Tamil Nadu state collapsed following heavy rain, killing 61 people, mostly workers.
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