Three large teams of the National Disaster Response Force (NDRF) are at the site, looking for survivors. The area, full of dilapidated buildings on narrow lanes, was also flooded in heavy rain in the past weeks.
Ten ambulances and fire trucks have arrived and are parked some distance away from the building as the lanes are too narrow for them to enter.
"We heard a loud noise. Everybody shouted, 'building is falling, building is falling'. I ran. It felt like a big earthquake," a teenager who saw the building fall told NDTV.
"This building must be 90-100 years old. I saw the bodies of some children. There were some seven-eight families in the building," another eyewitness told NDTV.
In visuals of the rescue operation, NDRF personnel in their bright orange safety gear are seen trying to remove concrete blocks as they probe the openings amid the debris for signs of life.
The authorities said this was a "level 2" incident - while level 1 is the most serious under the system that measures the severity of a building collapse.
Crowds thronged about the narrow lanes - where it would be extremely difficult for heavy machines to reach - and formed a human chain to pass down with their bare hands small debris like wooden blocks and bricks towards the outer area of the neighbourhood.
Building safety is a major issue in Mumbai, one of the world's most crowded cities next to Dhaka in Bangladesh, according to the World Economic Forum.
In May, the civic agency BMC in the country's financial and entertainment hub had identified 499 buildings as "dangerous"; it was 619 last year.