At least 40 other people were injured in the pre-dawn stampede when mourners thronged the home of Syedna Mohammed Burhanuddin, the head of the Dawoodi Bohra Muslim community, Mumbai Police Commissioner Satya Pal Singh said.
Burhanuddin died Friday at the age of 102.
Indian TV stations showed tens of thousands of white-clad mourners thronging the streets of Malabar Hill, an upmarket neighborhood in south Mumbai.
Singh said the stampede occurred when the gates leading to the leader's house were closed at about 1 a.m. The crowds surged forward, with many people getting crushed near the gates and with no way to escape.
Singh acknowledged that crowd management around the Syedna's home was poor and said police at the scene were badly outnumbered by the huge turnout of mourners.
The Syedna had succeeded his father in 1965 and led the community for nearly five decades.