The building collapsed Monday night in Mahim area of central Mumbai.
According to reports, those trapped inside are mostly children and senior citizens.
Recent monsoon rains may have caused the collapse.
A southwest monsoon hit Mumbai three days ahead of schedule and has been causing heavily flooding in the area since Sunday.
UPDATE: It's now being reported that one woman has died and three injured have been rescued from the collapse.
Ryan Broderick is a reporter for BuzzFeed News and is based in London.
Contact Ryan Broderick at firstname.lastname@example.org.
Got a confidential tip? Submit it here.