Fire crews rushed to the blaze, near the Wills Memorial Building, designed by Sir George Oatley.
The fire is reported to be in the Fry Building, which has been under refurbishment, in the shadow of Wills Memorial Building.
It is in the old part of the University, on Park Street in the city centre.
Surrounding roads have been closed and nearby buildings are understood to have been evacuated.
Avon Fire and Rescue FBU wrote on Twitter: “Thoughts with crews dealing with incident in Bristol right now. Hopefully not as bad as it seems. Plz give crews room to work & be patient if delayed”.
The Fry Building formerly housed the University’s School of Biological Sciences until 2014 and is on a triangular site between Woodland Road and University Road with the Wills Memorial Tower to the south.