The firefighter did not require medical treatment or to attend hospital and remained on duty after sustaining the injury.
The Northern Ireland Fire and Rescue Service said the cause of the fire at the derelict site is believed to have been deliberate.
A total of seven appliances attended the scene, three from Northland Fire Station, two from Crescent Link Fire Station and two from Strabane Fire Station and the fire took over three hours to extinguish.
Local SDLP Councillor Angela Dobbins said this was the second fire at the derelict site in Culmore in four days.
The councillor attended the scene last night and said the smoke coming from the fire was incredibly thick and would cause upset to people living in the surrounding area.
She appealed to those responsible for starting the fires to stop.
“They are going too far. This has been going on for years and it could result in one of their lives being put at risk.
“I would urge them to think about what they are doing to the people living in the area and the upset that is caused to them by these fires.
“I would also remind them they are using the resources of the Fire Service, which might be needed to deal with an emergency elsewhere.”
The former college, which has been vacant since 2004, has been earmarked for the development of a retirement village.
The councillor said the derelict site has become a ‘magnet for young people to get involved in vandalism and starting fires.’
“This is presenting dangers for the young people involved plus using up valuable resources of our emergency service.”
She added: “I am urging the Department for Infrastructure to sign off on their consultation to allow planning permission to be granted.
“This will allow the developers to push ahead with their plans for the retirement village and demolish these dangerous buildings before someone is seriously hurt or much worse.”
Colr. Duffy also urged parents to advise their children to stay away from the site.