At least 30 people are injured, including four who are stated to be critical by the hospital authorities.
The search operations are underway to rescue people who were still trapped under the debris, the BMC Disaster Control said.
As many as 34 victims died at Sir J.J. Hospital, while one succumbed to his injuries at the Nair Hospital.
Situated near the Dockyard Road, south Mumbai, the 33-year-old building was civic employees' staff quarters.
The building, which housed around 21 families, suddenly collapsed around 5.45 a.m Sep 27, catching sleeping residents unaware, the official added.
The 28-flat building, of which seven were unoccupied, and a ground floor warehouse was declared "extremely dilapidated" a few years ago.
Last month, it was surveyed by a BMC team which recommended urgent repairs after shifting the families living there.
Chief Minister Prithviraj Chavan who visited the crash site Friday night promised strict action against those responsible for the tragedy and announced an aid of Rs.1 lakh to the families of the deceased.
Mumbai Mayor Sunil Prabhu is supervising the relief operations with top BMC and fire brigade officials, and announced a compensation of Rs.2 lakh to the families of each of the deceased and free treatment of the injured in civic hospitals.
Acting on a complaint lodged by the civic body, the police have arrested a marquee contractor, Ashok Kumar J. Mehta for allegedly carrying out unauthorised modifications to the building.
Mehta was occupying the ground floor of the building and used it as a warehouse to store his decoration material. He has been charged with culpable homicide.
Police produced him before a magistrate and took his remand for three days.
--IANS (Posted on 28-09-2013)