Four others were injured but some saved their lives by scrambling out seconds before the collapse.
Fire crews and other rescuers saved many trapped workers but 12 died of their injuries, said Tanaji Kamble, spokesman for Mumbai's disaster management cell, AFP reported.
"The casualties could have been much higher but luckily some workers managed to escape before the building collapsed," Kamble added.
Authorities are looking into the cause of the blaze in the store in the suburbs of India's financial capital.
Building disasters are common in Mumbai, especially during the monsoon season from late June to September.
Millions live in cramped dilapidated properties because of high rental prices and activists say housing owners and builders often cut corners to save costs.
In August seven people died after a building collapsed in Mumbai following days of heavy rain. In July 17 people died when a four-storey building gave way in the northern suburb of Ghatkopar.
In 2013, 60 people were killed when a residential block came crashing down in one of Mumbai's worst housing disasters.