James Haswell, 48, passed away in hospital after collapsing in the second half of his team's Scottish Premier League game at Rugby Park.
The match was halted by referee Kevin Clancy with the teams drawing 1-1 and both managers agreed the game should be abandoned out of respect.
A statement from the club read: "Everyone at Kilmarnock Football Club extends their sincere condolences to the family and friends of the late James Haswell, who tragically passed away on Sunday 5th May after taking ill at Rugby Park during our match against Hibernian FC.
"In particular, our thoughts and prayers are with his widow Aileen and daughters Nicola and Stephanie.
"Aged 48, Jim had been a lifelong supporter of Killie and a season ticket holder for many years. His love of Kilmarnock FC was deep rooted and it is a tragedy for all who share his passion for the club that we have lost a truly devoted supporter."
Mrs Haswell said: "Jim lived for Killie and his family. He only missed one game in 17 years. He was the biggest Killie fan you could know."
The club added that arrangements to mark Mr Haswell's passing would be announced following discussions with his close family.