The game at Rugby Park was halted after 54 minutes with the score at 1-1.
"The referee, in consultation with SPL delegate Frank Coulston and the match commander at Rugby Park, decided to abandon the game," Kilmarnock chairman Michael Johnston told the BBC.
"The length of time the players were off the park was a problem but the overriding factor was respect for the fan and his family.
"We are awaiting news of his condition, and thank the supporters in the ground for their understanding of the situation."
The fan has been taken to hospital.
- Sports & Recreation
- Frank Coulston