The fire started in a bin in a nearby underpass, according to a spokesperson for the Northern Ireland Fire and Rescue Service (NIFRS).
They said the fire broke through into a tunnel and set fire to the dental building, run by Queen's University.
The building sustained smoke damage and some damage to its pipework, but there are no reports of injuries.
The blaze was reported about 20:20 BST on Thursday.
The NIFRS sent at least four fire engines to the scene, along with a team who specialise in dealing with hazardous materials.
The fire has been extinguished but a cordon was put in place for public safety.

She was performing in Verona in Italy when she spotted a woman in the audience with a tripod and camera filming her.
Talking to the woman in the crowd, Adele said: "Can you stop filming me with the video camera because I'm really here in real life and you can enjoy it in real life, rather than through your camera.
"Can you take your tripod down, this isn't a DVD, it's a real show and I'd really like you to enjoy my show because there's lots of people outside who couldn't come in."
The encounter was filmed by another fan in the audience, who posted it on Twitter.
Video courtesy of Madreeeh.

The 50-year-old was driving a Vauxhall Corsa when it was struck by a Jaguar S-Type at about 10:20 on Saturday in Irvine.
Two men are thought to have then abandoned the Jaguar before getting into a black Mercedes driven by a third man.
The 50-year-old is being treated at Crosshouse Hospital, where he is in a stable condition.
Police have appealed for witnesses to the crash, which was on Long Drive near the Newmoor Roundabout, to contact them.
Det Insp Mick Carr said: "A man requires hospital treatment following a serious road traffic collision. From what we understand, following the collision, two men abandon the Jaguar car and enter a black Mercedes car, driven by a third man. The men then leave the scene of the road traffic collision, heading north along the B7081.
"Our inquiries are ongoing to establish the circumstances surrounding the incident and we are yet to trace the black Mercedes which left the area.
"Anyone with information surrounding this collision is asked to contact police. If you witnessed the crash and have not yet contacted police, please contact officers with any information you may have."
A fire has damaged a dental building close to the Royal Victoria Hospital in Belfast.
[NEXT_CONCEPT]
Adele has stopped a concert mid-way through to tell a fan to stop filming her.
[NEXT_CONCEPT]
A man has been seriously injured in a hit and run collision in Ayrshire.