The Irish club released a statement on Sunday revealing that the coach had passed away overnight at the team hotel prior to their European Rugby Champions Cup clash with Racing 92.
The match, which was due to kick off at 3.15pm BST in Paris, has now been postponed.
"It is with deep regret that the Irish Rugby Football Union and Munster Rugby must advise the passing overnight of Munster Rugby head coach Anthony Foley, at the team hotel in Paris," read a statement from the IRFU.
"Munster Rugby management are liaising directly with Anthony's family and will provide them with any assistance and support required. The IRFU and Munster Rugby pass on our deepest sympathy to all of Anthony's family and friends. We 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."
Foley was appointed Munster head coach in 2014 having helped the province to their first European Cup in 2006.
Foley, a former back-row forward, also won 62 caps for Ireland during his playing career.