He said he was "disappointed" with the board's decision and "it would be a detriment to the show" if he was no longer event manager.
Asked if he would want to be involved in the show in some other capacity, he said: "I wouldn't want to play some part in the show. I think our company is the most successful equestrian-event management company in Australasia and we would only want to event manage the show."
The board reported a $108,000 annual loss last year, although the 2014 show was widely acclaimed a success. Cynthia Bowers, board chairwoman, said it had advertised for expressions of interest from event management companies "to deliver all or part of the show from next year".
A range of contractual and activity reviews were being undertaken and Sport New Zealand was also funding a broader activity review which would examine the "structure, governance and operation" of the show.
Hawke's Bay showjumping star Maurice Beatson said "it'll be a sad day if Kevin is not involved".
"He has vast contacts and that's why it's so successful, it takes a lot of manpower to run the show. You'd be going down a dangerous road if you got someone else to run it."
Ms Bowers, who is also deputy mayor of Hastings, said while she had "a lot of admiration" for Mr Hansen: "I think competitors come to the Horse of the Year Show because of the calibre of the event, not because of loyalty to Kevin".
Hastings Mayor Lawrence Yule said the board was responsible for deciding who ran the show.
"My understanding is they just want to make sure they've got the very best to run the event."
He said: "To go away from the Hansen family and all their experience and contacts, it would be a difficult thing to match, I would have thought."