The incident occurred at around 6 am near the Babugenu market in Dockyard Road area, fire officials said.
Four ambulances and 12 fire engines have been rushed to the spot.
Rescue operations are on to remove the people trapped under the debris, they said.
Four persons, who were rescued from the debris, have been admitted to the government-run JJ hospital.
A local Shiv Sena worker said there was a godown in the ground floor of the residential BMC quarters and some repair work was in progress.
Image: A video grab of the building collapse site in south Mumbai