The amateur rider fractured two vertebrae in his neck during a fall at the Cheltenham Festival.
The 37-year-old was riding Galaxy Rock for trainer Jonjo O'Neill in the Fulke Walwyn Kim Muir Challenge Cup on Wednesday when the pair fell at the first fence.
An air ambulance landed at the racecourse to treat the injured rider and he was taken to Frenchay Hospital in Bristol, where he has been undergoing treatment after being put into the coma.
He underwent surgery on Friday morning and Turf Club senior medical officer Dr Adrian McGoldrick has now confirmed: "The surgery was successful and he's still in an induced coma."
AP McCoy, who has been champion jockey 17 times told the BBC: "It's a dangerous sport and it's a sight you see that unfortunately crops up.
"We're very lucky we have excellent medical care. We just hope he's going to be OK."
McNamara is a leading Irish amateur rider who has won four races at the Cheltenham Festival in his career.