The European Champions Cup game has been postponed after the 42-year-old died overnight at the hotel.
Foley, who was capped 62 times by Ireland, captained Munster to Heineken Cup glory in 2006 and had been in charge of the side since 2014.
In a statement, Munster said: “It is with deep regret that the Irish Rugby Football Union and Munster Rugby must advise of the passing overnight of Munster Rugby head coach Anthony Foley, at the team hotel in Paris.”
The statement added: “The IRFU [Irish Rugby Football Union] and Munster Rugby pass on our deepest sympathies to all of Anthony’s family and friends and ask for privacy for the family at this sad time.
“As a mark of respect to Anthony and his family and to support players, management and staff, Munster Rugby have requested that today’s match against Racing 92 be rescheduled.
“Munster Rugby thank Racing 92, EPCR, broadcasters and partners, and the many fans who travelled to Paris for their understanding and support at this time.”