Forty people were also injured in the incident which occurred shortly after 1:00 am (1930 GMT Friday) at the residence of Syedna Mohammed Burhanuddin, who died at the age of 102 on Friday, it said.
It was unclear what triggered the stampede.
Buhranuddin, who was to celebrate his 103rd birthday in a few weeks, died of a heart attack at his home. He was a leader of the Dawoodi Bohra community, a sect of Shiite Islam.
The disaster comes just months after some 115 devotees were crushed to death or drowned in October near a Hindu temple in the central state of Madhya Pradesh.
India has a long history of deadly stampedes at religious festivals, with at least 36 people trampled to death last February as pilgrims headed home from the Kumbh Mela religious festival on the banks of the river Ganges.
Some 102 Hindu devotees were killed in a stampede in January 2011 in the state of Kerala, while 224 pilgrims died in September 2008 as thousands of worshippers rushed to reach a 15th-century hill-top temple in Jodhpur.