McGoldrick said: "We can confirm that amateur rider JT McNamara suffered two fractured vertebrae in his neck.
"He is currently in theatre at Frenchay Hospital in Bristol. There will be no further news until tomorrow and we will keep everyone updated.
"His wife Caroline is with him."
Cheltenham, the British Horseracing Authority and Jonjo O'Neill, the trainer of Galaxy Rock, have agreed the Injured Jockeys Fund will issue further information on the rider's condition when appropriate.