"The number of dead is now 11," said a police official who asked not to be identified.
The official earlier said at least 20 people were believed to be trapped, but no clear figure had emerged by late Tuesday.
He said seven women were among the dead, as well as a child and three men.
Mumbai's chief fire officer, AD Jhandwal, said that about 40 people had been rescued from the rubble.
"We have searched the rubble and till now no more bodies have been found," Jhandwal said.
Suresh Karande, a senior official of the housing authority of Maharashtra state, of which Mumbai is the capital, said the collapsed structure was almost 90 years old and had been repaired with state funds two years ago.
Situated in Mumbai's south-central Nagpada suburb, the building had housed 22 families and a number of shops, police said.
Heavy machinery was brought in to lift rubble as rescue teams searched for survivors.
Local officials this week released data that about 19,000 high-rise buildings in South Mumbai are "old and dilapidated".