Most of the injured people were taken to Saifi Hospital where 17 people, including two children, were declared dead. One person died in Cumballa Hill Hospital.
At least 20 people, who suffered injuries, were treated and allowed to go, while another three have been admitted for treatment, BMC Disaster Control said.
Sadanand Date, joint commissioner of police (law and order) confirmed the death of 18 people in the incident.
"The incident took place at around 1.30am when the gate of the Saifi Mahal was closed for last glimpse, but followers kept coming outside the bungalow. Due to this many felt suffocated and later a stampede broke out," said Krishna Prakash, additional commissioner of police (south region).
The cause of the stampede is not clear but police officials say death toll may rise.
Syedna Mohammed Burhanuddin died following a cardiac arrest on Friday. He was 102 and his funeral is scheduled later this morning in Bhendi Bazaar in south Mumbai.
(With IANS inputs)