The building is in South Street, a residential area near the town centre.
On the PSNI Ards Facebook page earlier on Sunday evening, officers said: "We fear the wall may collapse at any time due to high winds."
A spokeswoman for the Department of Infrastructure said the remainder of the structure is considered unsafe.
She said the road has been closed to protect the public.
Meanwhile, there has been a serious crash involving a fallen tree on the Belfast Road in Comber, County Down.
A woman was seriously injured when a tree fell on her car.
Police said it is likely the road will remain closed overnight.
"The remains of the fallen tree are too dangerous to work on with darkness and continued high winds," they added.
A derelict building has collapsed in Newtownards, County Down, shortly after police closed the road due to fears the wall was going to fall in high winds.