A federal government minister said the death toll was likely to rise.
Indian media reported the Home Ministry had called the separate blasts in three busy locations in India's busy financial capital a terror attack.
One blast was in the crowded neighborhood of Dadar in central Mumbai. The others were at the bazaar, which is a famed jewelry market, and the busy business district of Opera House, both in southern Mumbai and several miles (kilometers) apart, a police official said.
All three blasts happened from 6:50 p.m. to 7 p.m., when all the neighborhoods would have been packed with office workers and commuters.
The blasts - if confirmed as a terror strike - would mark the first major attack on Mumbai since 10 militants laid siege to India's financial capital for 60 hours in November 2008.
The Associated Press contributed to this report.