Fire engines and emergency teams rushed to the scene in the city's southern business district amid reports that some people were still trapped inside.
Television pictures showed several people standing on balconies, desperate to be rescued as navy helicopters hovered overheard and thick smoke billowed across the city.
The building is the headquarters of the government of Maharashtra state, of which Mumbai is the capital, and the chief minister's office was among those damaged in the blaze.
Mumbai police could not confirm any immediate casualties, but the NDTV news channel reported that at least three injured people had been taken to a local hospital.
Mumbai's fire fighters called for back-up as they struggled to control the blaze, NDTV reported.
The Press Trust of India news agency said the fire, which began on the fourth floor and quickly spread to the top of the seven-floor building, was suspected to have been caused by an electrical short-circuit. Government ruled out sabotage.
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