Thirteen minutes into the game at Old Trafford, Gueye, 36, and Keane, 32, had a coming together in their own box.
Keane appeared to shove Gueye, to which the midfielder responded by slapping his teammate, earning a straight red card from referee Tony Harrington for violent conduct.
Everton goalkeeper Jordan Pickford had to drag a furious Gueye away from Keane before he eventually walked off the pitch.