TV presenter Cherry Healey and Love Island star Ovie Soko also left during the penultimate episode of the Channel 4 show which tests competitors’ physical endurance and mental strength.
In one challenge recruits were tasked with wrestling an opponent and getting them outside a makeshift ring filled with mud.
Norris, 38, took on two-metre tall basketball player Soko, 33, who won the bout and ripped Norris’s shirt in the process.
Former professional boxer Anthony Ogogo was the last competitor standing after all six recruits faced off in the ring.
After the challenge, Norris requested a medic and was sent to a doctor who said he needed to medically withdraw him from the show.
He said Norris had “a lot of spasm” going down his neck which was “likely to increase”.
He told Norris: “Your mobility is going to get more restricted, and you’re going to be at risk of doing yourself more damage.”
Healey, 43, was the first to leave during Sunday night’s episode and told presenter Jason Fox: “It’s been life-changing, but I know when the line is and that’s fine. I thought about this long and hard.”
Soko left while “on the run” in a challenge that split the recruits into two teams and tasked them with finding their way to safety at night while being pursued by a hunter force made up of ex-military members.
After he engaged in a heated exchange with reality star Georgia Harrison, he said: “I’m done… I’m going to hand my armband in.”
The recruits were also given a chance to speak to their loved ones during Sunday night’s episode but Ogogo decided not to as it would make him look “soft”.
The final instalment of Celebrity SAS: Who Dares Wins airs on Monday at 9pm on Channel 4.