He is not thought to be seriously hurt, but a decision was taken to airlift him because of the remote location.
The island is a popular tourist spot reached by a rope bridge suspended almost 100 ft (30 m) above the sea.
Emergency services called a helicopter rather than taking the risk of walking the casualty back over the rope bridge.
The Royal Navy search and rescue rescue helicopter was sent from its base in Prestwick, Scotland.
Its crew transferred the injured man, who is in his 60s, to the Causeway Hospital in Coleraine, County Londonderry.
A spokesman for the hospital said the patient is in a stable condition.
A man has been airlifted to hospital by Royal Navy helicopter after he fell while walking on Carrick-a-Rede island off the coast of County Antrim.