Walsh has sustained a compound fracture of his right humerus, the bone in the upper arm, after tumbling from Abbyssial during the JCB Triumph Hurdle.
Walsh was leading the field over the second hurdle when he suffered a painful spill, bringing down stablemate Adriana Des Mottes in the process. The Irishman was able to get back to his feet and walk gingerly to the ambulance, but could be seen holding his arm.
The rider was later waiting to undergo surgery on the open fracture at Gloucester Hospital.
Walsh's understudy at the Willie Mullins yard, Paul Townend, the rider of Adriana Des Mottes, rode in the second race but was then also stood down for the day, with David Casey taking the rides on Briar Hill and On His Own in the Gold Cup.
"He wasn't feeling too well," Mullins said of Townsend. "The best thing to do was to not ride."