Mumbai, formerly known as Bombay, is the capital of the state of Maharashtra, the most populous city of India, and by some measures the most populous city in the world, with an estimated population of about 13 million.
"Local police have arrived at the site of the incident and have started an investigation," the source said, adding that a total of six firefighter crews and four ambulances had been dispatched to help the rescue effort.
Some people may still be buried under the debris of the building, the police said.
It is the fifth reported building collapse in the commercial and entertainment capital of India in over a month.
At least eight workers were injured when a basement beam collapsed at a construction site on Sunday. Two women and three children were killed in a collapse of a five-story building August 15.
The worst incident occurred July 18, when a section of an apartment building collapsed, killing at least 29 people.
