He performed last year at the Folly Theater and died Thursday after checking into St. Luke's Hospital on Nov. 27 with breathing problems, The Kansas City Star said.
The Web site jaymcshann.com says he was born January 12, 1916.
McShann was traveling to Omaha, Neb., in 1936 when he stopped in Kansas City. He got a gig two days later.
Born in Muskogee, Okla., McShann taught himself to play piano by ear. A Kansas City insurance man financed McShann's big band in 1939. Charlie Parker played saxophone.
McShann was drafted in 1944. After the war he found a big band too costly, so he played in small groups. From the 1970s to the '90s he performed frequently in the United States, Europe, Australia and New Zealand. Performances in Kansas City drew enthusiastic fans.
McShann was one of the jazz greats interviewed by documentary filmmaker Ken Burns for the "Jazz" series on PBS.
Three daughters and his longtime companion and manager Thelma Adams survive McShann.