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.