Dozens of calls were received about the fire which has damaged the fifth floor and roof space of the University of Bristol building in Colston Street.
Four fire engines, a turntable ladder and more than 40 firefighters have been dealing with the blaze, Avon Fire and Rescue said.
It was thought no-one was inside and there were no reports of any injuries.
Eyewitnesses said it started as a small fire in one corner but very quickly took hold.
"We saw tiles falling off as the fire brigade arrived and not long after the wall on the south-west side of the building started to buckle," said an eyewitness called Ellie.
"Nearly two hours after it started the whole roof was completely gutted."
Richard Meal, who works on the 13th floor of the neighbouring Colston Tower, said: "As the fire took hold, tiles from the roof were crashing down from the roof on to the fire engines below.
"The top couple of storeys of the building are gutted and blackened and the fire is still burning over two hours later."
A university spokeswoman confirmed the fire at 33 Colston Street was in a residential block.
"Students have been evacuated from the building and as far as we are aware no-one has been hurt," she said.
"Students resident in the building will be rehoused and supported through the process. We will be working with Avon Fire and Rescue Service to determine the cause of the fire."
Avon and Somerset Police have asked motorists to avoid Colston Street and the surrounding roads.
A major fire has ripped through the roof of a block of student accommodation in Bristol city centre.