The report says the incident took place as the Flybe flight from Birmingham, carrying 47 passengers, was approaching Belfast City Airport in gusty conditions in February.
The 46-year-old pilot had shortly before checked that his prosthetic lower left arm was securely attached to the yoke clamp, but as he performed a maneuver just before touchdown the limb became detached.
The Air Accidents Investigation Branch said Thursday he then moved his right hand to the yoke to regain control. Winds caused the plane to land heavily with a bounce.
No one was hurt in the incident.