The Tri-Lakes News reported the 83-year-old Williams appeared early in the show at the Moon River Theatre and vowed to return next year to celebrate his 75th year in show business.
Williams told the crowd that bladder cancer is, "no longer a death sentence" and that he would survive.
The "Moon River" singer has not yet started treatment, according to the newspaper.
Williams' appearance Saturday was a surprise and brought a standing ovation from a nearly full house.
The golden-voiced singer had a string of hits in the 1950s and 60s, including "Can't Get Used to Losing You" and "Butterfly," but he is best known for his version of "Moon River." He earned 18 gold and three platinum albums in his career.
The Associated Press contributed to this report.