The building, 'Yusuf Manzil' at Lamington Road, caved on Tuesday evening after one of its main pillars weakened due to some construction work carried out by a shop on the ground floor of the building.
Five others who were rescued suffered minor injuries and were treated at the hospital. Among those rescued was a month-old infant.
"We have rescued four people so far from the building. Of the four people, we have rescued a month-old infant and an 80-year-old woman," said Pratap Damodar Kargupikar, Chief Fire Officer, Mumbai.
Milind Deora who is the elected lawmaker from Central Mumbai visited the spot and said that the actual cause could be ascertained only after the investigations.
"Some people say a shopkeeper began some illegal construction after pulling down the shutter of his shop. The authorities will enlighten you with the actual cause after the investigations," he added.