One other person was seriously injured in the blaze, which broke out early Thursday morning, Mumbai police spokesperson Ashok Dudhe told AFP.
"The primary reason for the fire seems to be a short circuit. But officials will have to establish the exact cause once investigations are complete," he said.
It was the latest deadly fire to hit Mumbai in recent years.
In June last year, a fire in a high-rise apartment block killed seven people after they became trapped in a lift on the upper floors.
A month earlier, four firefighters were killed in a blaze at another building.
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