Mukesh Ambani received a death threat by email late on Friday.
The tycoon was told that he would be shot dead if he did not pay up a sum of Rs 20 crore.
The Reliance group chairman's head of security filed a first information report (FIR) with the Gamdevi police station in south Mumbai against an unidentified person who also claimed that his group had some of the best sharp shooters in the country.
A PTI report quoting a police official said a case had been filed under Indian Penal Code (IPC) Sections 387 (put- ting a person in fear of death or of grievous hurt in order to commit extortion) and 506 (2) (criminal intimidation).
Police have launched a manhunt to nab the person who sent the e-mail.
Ambani is the richest person in the country. The Bloomberg Billionaires' Index has estimated his net worth at Rs 84,800 crore. The Centre has already granted Ambani and his family Z+security.
Back in March, the Supreme Court had directed authorities to provide him and his family members a higher level of security in India and abroad. The Ambani-family bears the expense for the security cover.