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.
A fire has damaged a dental building close to the Royal Victoria Hospital in Belfast.