The scare, on a Flybe flight from Birmingham, came as the Dash 8 aircraft, with 47 passengers on board, was approaching Belfast City Airport in gusty conditions.
The Air Accidents Investigation Branch (AAIB) report said the 46-year-old pilot was flying the plane manually after making sure his prosthetic lower left arm was securely attached to the yoke clamp he uses when he is flying the aircraft. It said shortly before touchdown "his prosthetic limb became detached from the yoke clamp, depriving him of control of the aircraft".
The captain quickly moved his right hand from the power levers on to the yoke to regain control.
The report went on: "With power still applied and possibly a gust affecting the aircraft, a normal touchdown was followed by a bounce, from which the aircraft landed heavily."
No-one was hurt and the plane was not damaged in the incident on the evening of February 12 this year.