He was airlifted from the scene after the crash in the 400cc Supersport race just after 16:00 BST on Saturday.
An Irish Coastguard helicopter flew the injured rider to the George Best Belfast City Airport.
An ambulance met the crew at the airport and transferred the patient to Belfast's Royal Victoria Hospital.
In a statement, the Armoy Motorcycle Road Racing Club said: "We are not yet aware of the extent of the injuries sustained by the rider."
A motorcyclist competing in the Armoy Road Races in County Antrim is critically ill in hospital after suffering a head injury in a crash.