Six cases have been confirmed in the red squirrels since 2006, from Dumfries and Gallow to the Moray Firth in places like Pitlochry, Speyside and Nairn.
Professor Anna Meredith of the Royal (Dick) School of Veterinary Studies at the university is now leading the research into the infection.
She said: "We discovered this because of our general surveillance of squirrels in Scotland which involves dead squirrels being sent to us. It was part of our routine scanning for squirrel pox. We weren't going out looking for it, but we have managed to collate these six cases over the years.
"It is difficult to say how quickly they die from it, but generally this type of disease is very slow and chronic. We have had sightings and pictures sent in of squirrels feeding in people's gardens with very similar lesions.
"So it is very different from squirrel pox which is a rapid epidemic killing them quickly. But the six we have seen were all adults in very poor condition. So they do succumb."
The bacterium involved hasn't previously been reported in relation to leprosy in animals.
Prof Meredith said there was no pattern and their distribution suggested it wasn't a localised issue. "But leprosy is a difficult disease to catch. It is not highly infectious. So we need to find out where they are picking up the bacteria and what the risks are. It is potentially worrying."
She said current estimates are that there are 120,000 red squirrels in Scotland, about 75 per cent of the remaining UK population. She said they are at risk from grey squirrels on two fronts: "Grey squirrels provide completion for resources and habitats, but you have to add the pox virus which the greys carry without any symptoms, but kills the reds rapidly. The pox is up as far as the central belt. We only got it in Scotland in greys in 2007 and in 2008 we saw it in reds.
"We are very worried it could spread north. We need to keep the greys out of there."