Craigmillar Community Arts on Newcraighall Road has used the basement for storage for several years, with staff going in and out to retrieve equipment.
But it has now been closed off indefinitely because the charity cannot afford to have the area made safe.
And concerns have been raised that the asbestos has been exposed for several years.
The group's arts coordinator, Mike Greenlaw, said: "We've had a survey of the building done, as all public buildings are expected to have. The survey showed up that there was some asbestos insulating pipes in the cellar of the arts centre. As soon as it was drawn to our attention that there was the possibility that asbestos was there, we closed it to normal use.
"We had the survey done and now all we think we can do is simply keep the place totally locked, with a key kept off the premises, and that's probably what we'll have to do until we can raise the money to get it removed."
He said it would probably cost between 4,000 and 8,000 to make the basement safe.
Mr Greenlaw said he did not know if there was any risk to people who had been into the cellar.
The building, a former church, was used by the group's forerunner, the Craigmillar Festival Society, from 1976 until 2002, and the basement was more widely accessible to members of the public when it was used for craft workshops for several months in 2001.
One art worker who carried out workshops in the basement, but did not want to be named, said he had heard of the risk of asbestos in 2001, when he spoke to a surveyor while he was having a cigarette break. "The surveyor said to me 'If the smoking doesn't kill you, the asbestos really will'. The lagging from the pipe was only three feet from my workspace."
He said he had told centre management about his fears at the time, and was told it was not asbestos. "My concern is for hundreds of people that have used that place over 35 years and could have been in contact with it, because asbestos must have been in pretty high concentration. I used to see the flakes falling from the lagging." However, Mr Greenlaw said he was not aware of the issue being raised then, and added: "If somebody had said, 'there's potential of asbestos in here, you should get it checked,' we would have done it. I do not think I'd have just said 'Aye, so what?'
"Way back in the days of the Craigmillar Festival Society, in the late-70s, there was someone who did some work in the cellar, and I have a recollection of there being a suggestion of asbestos then – and that had been proved not to be the case."