The passenger, who was not named, was flying to London from Dubai on Flight BA0104 yesterday.
A Metropolitan Police spokeswoman said: "Officers attended and found a 21-year-old man who had assaulted a passenger. The man was arrested on suspicion of actual bodily harm and being drunk on board an aircraft.
"He was taken to a west London police station and has been bailed to a date in late May. The injured passenger received medical assistance for a minor injury at the scene."
As a token of appreciation, he was allowed to sit in the cockpit by the pilot, the Sun reported today.
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Chris posted pictures on social media of the bite mark, along with one of himself giving the "thumbs up" as he sat in the cockpit once the plane had landed and was safely in a hangar.
He wrote on Instagram: "That time when you help restrain and handcuff a nutter at 40,000ft. He bites you, but it's all OK because Captain Kendal lets you sit in the cockpit."
"Incredible team on the flight, especially Hayley, who put herself in harm's way to protect passengers. Thanks to British Airways Captain Kendal for showing me the cockpit. The bite and A&E were almost worth it."
British Airways thanked Chris, saying: "We hope you are all right. I'm sure Hayley would've appreciated your assistance on board. Thanks."
The airline said the matter was now being dealt with by police.