The wife and son of noted criminal lawyer Rizwan Merchant, who represented actor Sanjay Dutt in court when he surrendered last month in connection with a 1993 Mumbai blasts case, are among those killed.
Mumbai BJP President Ashish Shelar said there was construction going on below the ground floor of the building which may have weakened the structure.
The building collapsed a day after heavy rain lashed the city. The injured have been shifted to Bhabha Hospital in suburban Bandra, KEM and at the Sion Hospital.
The Altaf Manzil building, which is located near the famous Mahim dargah or shrine on Cadell Road, had a Maruti car showroom on its ground floor.
Several cars parked nearby were also crushed by debris.
In April, 74 people were killed when an illegal building collapsed in Mumbra in Thane.