Rescue workers said the dead included two children, adding that the survival chances of those trapped diminished with every hour.
Civic authorities blamed faulty repair work being carried out in the building for the accident.
J Phatak, a senior city official, said residents reported extensive renovations to the building by a jewellery shop on the ground floor of the building.
The building housed several shops and a clinic in addition to residences.
Old or poorly constructed buildings crumble in Indian cities during the monsoon rains every year.
In Mumbai, civic authorities - often accused of poorly implementing building codes - maintain a list of dangerous buildings. However, the one which crashed down on Wednesday was not on it.
In January, 11 girls were killed when their school residence collapsed in the western state of Gujarat.