The show was due to go ahead on Sunday night at the Glasgow venue, but has now been switched to Tuesday.
The Scots entertainer took to social media to break the news to fans on Saturday after suffering the freak injury.
And he revealed that he has undergone an MRI scan after the incident.
The 52-year-old has been forced re-arrange his show in Bristol which was due to go ahead on Saturday night, on medical advice.
On Instagram, Barrowman said: “I’m devastated to have to tell you that due to a severe neck injury, which has made it impossible for me to sing and move, I’ve been rushed to hospital for a diagnosis.
“The doctors have advised me to not perform this weekend while I try and recover, so I’ve had to make the very difficult decision to cancel my performances at the Bristol Hippodrome on Saturday, November 30 and at the SEC Armadillo, Glasgow, on Sunday, December 1.
“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.
“We have thankfully managed to open the Oxford New Theatre concert (Sat, December 14) for Bristol audience members to transfer to, and we have managed to move the Glasgow date to Tuesday, December 3 so I really hope you will be able to still see me have A Fabulous Christmas.
“All my love, John x.”
He added: “Heading to hospital for an MRI scan on my neck but just had the great news that the album entered the charts.
“I’ll Keep you all posted on my progress – Bless you all and thanks for all your good wishes.. JB.”
Barrowman, who made the final three in the jungle last year, did not reveal how he suffered the injury.