At least six fire engines were involved in extinguishing the blaze which hit the university’s Fry Building.
Balfour Beatty started on site early last year on a £19m contract to renovate and extend the Grade II listed building.
The new School of Mathematics was topped-out in November and was due to be finished and open in time for the new academic year in September.
An Avon Fire and Rescue statement on Saturday night said: “Firefighters have extinguished a fire at a five storey University of Bristol building in Woodland Road, Bristol.
“The service received more than 25 emergency calls reporting a fire at the Fry Building and sent crews from Temple, Southmead, Bedminster, Kingswood, Avonmouth, Chew Magna, Bath and Portishead fire stations to the scene.
“Firefighters from six fire engines, two turntable ladders and support vehicles tackled the fire which involved the top floor of the building.
“The building is currently under renovation and no one was believed to have been in the building at the time of the fire. There have been no reports of any injuries.
“Although the fire has been extinguished crews remain on scene damping down and checking for hot spots. The cause of the fire in not currently known but will be investigated.”
A Balfour Beatty spokesperson said: “A fire broke out in the Fry Building at just after 5pm yesterday evening (Saturday 6th January). We are currently undertaking refurbishment works to the building on behalf of the University of Bristol.
“Everyone has been accounted for and the fire was extinguished by Avon Fire & Rescue by 20:00 last night.
“The safety of the public and our workforce is always our primary concern. As an investigation is ongoing it would be inappropriate for us to comment further at this time.”
