DGA president Louise Taylor said the testing was undertaken to comply with the new Health and Safety at Work Act 2015.
No asbestos was found in the air, but the results came back positive for the rafters and window sills.
"The advice is that the health risk is very low,'' Taylor said.
"However, due to our obligations under work safe [legislation], we have made the difficult decision to cease classes at Willis St until we have further advice and a plan of how to proceed.
"The property owner is investigating but warns it is likely it will not [be] viable to have repairs made to the building to eliminate the risk from asbestos.''
The testing was carried out by Southern Insulation and the gym was closed as soon as the results were known.
The closure affects more than 150 gymnasts who train at the venue. They range from pre-school children to gymnasts in their 20s.
The club is facing an "uphill battle'' to find a medium to long-term solution.
"We have had great support from the other two gymnastics clubs that are in the city, which is College Street and St Bernadette's. Both of those clubs have come to the party and offered us training times and space.
"We are able to get our gymnasts into those facilities to train, so we are able to continue over the next little while at least.
"We've had a plan over the last few years to try to establish a central club which would mean all of our programmes can operate together.
"This has proven pretty challenging given the standard of the buildings around the city and our requirements in terms of size,'' Taylor said.
"What this decision, in terms of Willis St, really means is we have to escalate that process. We are now in a position where we require a temporary building as well as our long-term goals.
"But at the moment our priority is to find a temporary facility that can cater to our Willis St programme.''
The DGA operates out of two other buildings - the old Caledonian gym and the Vogel St gym.
The DGA, the Otago Hockey Association and Mountain Biking Otago commissioned a feasibility study looking into the prospect of building a multi-use facility at the back of Logan Park High School.
The report, released in December, put the cost at $10.3 million.
The project was "still moving forward'' but a decision was a long way off.
"In the meantime, we are also talking to the Dunedin City Council about alternative options.''
