The disaster, which occurred in the northern suburb of Ghatkopar on Tuesday morning, was the latest to shine a spotlight on poor construction standards in India.
"Seventeen have died and 28 people have been rescued," Tanaji Kamble, a disaster management spokesman for Mumbai's civic administrative body, told AFP.
Some bodies were found during the night. Rescuers, using diggers, sifted through the debris on Wednesday morning in the hope of finding more trapped survivors in the block of apartments.
Building collapses are common in India, especially during the monsoon season from late June to September.
India's financial capital is particularly vulnerable with millions forced to live in cramped, ramshackle properties because of rising real estate prices and a lack of housing for the poor.
The city has been hit by several deadly building collapses in recent years, often caused by shoddy construction, poor quality materials or ageing buildings.
The chief minister of Maharashtra state, of which Mumbai is the capital, ordered an investigation into the latest incident after reports that renovation work was going on at the site at the time of the collapse.
In 2013, 60 people were killed when a residential block came crashing down in one of Mumbai's worst housing disasters.
A dilapidated building left 12 people dead when it collapsed near the city in August 2015. Nine people died the same month when another old three-storey building collapsed in monsoon rain in the Mumbai suburb of Thakurli.