The centre opened five years ago and was built by Barr Construction.
Structural engineers have discovered “structural weakness in the block work” at the ice rink.
The rest of the facilities at the centre are open and will continue to operate as normal.
A council spokesperson said: “We have been notified by our contractor that the ice rink is facing some structural issues and must be closed for the next few weeks to ensure public safety.
“The contractors are working with Active Stirling and ourselves to resolve the situation as soon as possible.
“We apologise for any inconvenience caused and are doing all we can to ensure the safety of the ice rink is restored as soon as possible.”
A spokesperson for the centre said: “Our contractors have advised that the ice rink must be closed with immediate effect and for the next few weeks while structural repairs are undertaken to ensure public safety.”