The 37-year-old was placed into an induced coma after coming off his horse, Galaxy Rock, in the Fulke Walwyn Kim Muir Challenge Cup.
He was airlifted to Frenchay Hospital in Bristol, where he is being cared for in a specialist unit for spinal injuries.
"JT has suffered a serious neck injury," said Dr Adrian McGoldrick, chief medical officer for the Irish Turf Club. "He is being looked after at the regional spinal unit but as yet he is still waiting for a scan."
Fellow rider AP McCoy has paid tribute to McNamara in the wake of the incident and wished him a speedy recovery.
"It's a dangerous sport and it's a sight that you see that unfortunately crops up; we're very lucky we have excellent medical care. We just hope he's going to be okay," he told BBC Sport.
Racing on the third day of the festival was postponed for 30 minutes as the jockey was treated by medical staff.