Kevin Wilson alleges the 68-year-old singer told him: "We have too much colour on stage".
The lawsuit states the dancers were fired from Cher's Dressed To Kill tour after also informing managers that another dancer assaulted an unidentified woman in a hotel room while on tour. The choreographer and two other dancers are seeking $10m (£6.1m) in damages. Cher's publicist Liz Rosenberg denies the allegations and says there is no truth to them. She told TMZ: "These are ridiculous allegations. They couldn't be further from the truth."
Two of the plaintiffs, who are black, say their race was a motivating factor in their dismissal. The third dancer cites age discrimination as a factor in her firing. Cher has been forced to postpone recent shows to later in the year after suffering from a virus.