"This is not feasible in a team environment where all the riders must work closely together with team management to get the best results, and consequently this leaves no way to go forward with him in the squad at present," an ESNZ statement said.
ESNZ said Nicholson's behaviour at the world games "fell far short of what is expected" in its code of conduct. However the door remains open for a return to the high performance group.
Nicholson, 53, is a five-time winner of the prestigious Burghley trial and a member of the bronze medal-winning team at the London Olympics in 2012.
"There is no question that Andrew is an outstanding rider, but our role is to look out for the whole team," ESNZ chief executive Vicki Glynn said yesterday.
Tim Price will be New Zealand's only high-profile rider at the Kentucky four star event this weekend.
Price, who won the Luhmuhlen four-star event last year, is riding his quality horse Wesko. The other NZ rider at Kentucky is Emily Cammock on Dambala.