The singer and actor tweeted he was “devastated” by the injury which he said “had made it impossible for me to sing and move”.
The 52-year-old said he had been advised by doctors to cancel his Fabulous Christmas shows this weekend.
“I am so disappointed and upset as I was looking forward to seeing you all, I feel I am letting everyone down, but it’s simply not possible for me to do the show in my current condition,” he wrote on his Twitter and Instagram accounts.
The Doctor Who and Torchwood star was due to take to the stage at the Bristol Hippodrome on Saturday night and at the SEC Armadillo in Glasgow on Sunday.
He later posted an update on his condition on social media on Sunday, revealing he had had an MRI scan “and they’ve found the root of the problem”.
“Hopefully a series of intraspinal injections will reduce inflammation and get me back up and running again in time for Monday’s show in Manchester,” he wrote.
“#NotFeelingSoFabulous but a massive blessing to have you all out there sending your positive thoughts and messages. Thank you.”
Fans responded with scores of posts wishing the actor and TV presenter well.
“Just focus on getting better,” wrote one.
Another said: “Sorry to hear you are injured and in pain. Hope the injections do the trick and you are up and pain free really soon. Take it easy xx.”
Bristol Hippodrome tweeted that fans with tickets to Saturday’s show could exchange them to a new date at Oxford New Theatre on 14 December.
The SEC Armadillo said Sunday’s show had been moved to 3 December for which original tickets would still be valid, adding: “However, a full refund can be obtained from point of purchase”.