Trainer Nicky Henderson and owner Michael Buckley came to the decision having agonised over it for days since the nine-year-old impressed greatly in his first ever run on the Flat at Southwell.
Having fallen in three of his last four outings over hurdles, the choice came down to asking the former champion to return to jumping or potentially spending the rest of his career on the level.
Henderson had announced on Tuesday that Constitution Hill would have a schooling session on Wednesday and following that connections came to their conclusion.
In a statement Henderson said: “Michael Buckley and I have not surprisingly spent a lot of time soul searching and thinking over Constitution Hill’s future and have sadly concluded that he will not be running in the Unibet Champion Hurdle the week after next.”
More to follow.