Prabhat Rahangdale, said nine people had been rescued but dozens more were believed missing under rubble.
The city's chief fire officer, Prabhat Rahangdale, said nine people had been rescued but dozens more were believed missing under rubble after the structure gave way mid-morning in the northern suburb of Ghatkopar.
"Entire ground and four floored residential building collapsed. About 30 to 40 persons suspected to be trapped. Until now nine persons (have been) rescued and sent to hospital," Rahangdale said in a text message to AFP.
Tanaji Kamble, a disaster management spokesman for Mumbai's civic administrative body, said there had been no reports of any deaths and the nine admitted to hospital had minor injuries.
"Our rescue teams are conducting search operations to help people trapped inside," he told AFP.
Building collapses are common in India, especially during the annual monsoon season which usually runs from late June to September.
Millions of Indians are forced to live in cramped, ramshackle properties because of rising real estate prices and a lack of housing for the poor.
A dilapidated building killed 12 people when it collapsed outside Mumbai in August 2015.
Nine people died the same month when another old three-storey building collapsed in monsoon rain in the Mumbai suburb of Thakurli.
At least four people were killed in two incidents in April and August last year when buildings collapsed in the city.