The star was among people evacuated from the Scottish Event Campus' (SEC) Armadillo on Saturday evening.
In a tweet he said there was "smoke bellowing from the back of the venue".
The Scottish Fire and Rescue Service said they were called to a small fire at around 18:00 but it later spread to external cladding. They added that no one was hurt in the incident.
Firefighters were on the scene of the fire until about 22:30.
Both Mr Watson and the SEC later took to social media to confirm that the concert had been cancelled.
The singer said ticket holders would be contacted by the venue.
Mr Watson went on to thank the fire crews involved in extinguishing the blaze.
In a tweet to one of the firefighters, he said: "Well done to u and your team for dousing the flames at the SECC today! We all appreciate the job the fire service does x"
It is understood that Bob Dylan's gig at the venue will go ahead as planned on Sunday.
Singer Russell Watson was forced to cancel a concert in Glasgow after a fire broke out at the venue.