The National Trust said it had taken the decision after a "small landslide".
It added the site would remain closed until a proper survey could be conducted of the incident.
The bridge was first erected by salmon fishermen in 1755.
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It is almost 100ft (30m) above sea level and a favourite attraction for visitors and operated by the National Trust.
In 2017 the bridge was replaced as part of regular conservation works.
In a Tweet the National Trust said: "Due to a small landslide on the island at Carrick-a-Rede we have taken the decision to temporarily close @NTCarrickarede. The safety of our staff and visitors is paramount therefore the bridge will remain closed until all necessary specialist surveys have been completed."