The show's spokesperson was unable to give a reason for the late decision, but confirmed that producer Keith Turnispeed is looking for alternative dates.
Chita Sings is an expanded version of Rivera's critically acclaimed cabaret show seen at Feinstein's at the Regency in New York.
Accompanied by conductor David Krane, Rivera was due to perform many of the songs she made famous, including "A Boy Like That" from West Side Story (Rivera created the role of Anita in that classic musical).
A two-time Tony winner, Rivera's career spans over 50 years. She was last seen on the London stage in 1999 when she reprised her performance as Roxie Hart in Chicago. Other acclaimed performances include the musicals Nine, Kiss of the Spiderwoman and The Rink as well as the original Broadway cast of Chicago. Chita Sings also features cabaret performer Jeff Harnar, who serves as the evening's host. Earlier this year Harnar played London's small Jermyn Street Theatre with his show The American Songbook in London, under whose banner producer Turnispeed was to present Chita Sings in London.