Thomas Cook flight TCX3876 from Glasgow to Dalaman arrived at Gatwick, after an on-board incident, at about 11:15.
Sussex Police boarded the plane at 11:45 and arrested a 34-year-old man. Two women with him were not detained.
There were no reports of injuries or damage. Thomas Cook said the plane remained at Gatwick until 13:05.
A statement from Gatwick Airport read: "Gatwick Airport can confirm that a flight was diverted to the airport and two individuals were removed from the flight.
"The matter is now being dealt with by Sussex Police."
A spokesperson for Thomas Cook Airlines said: "We have a zero tolerance policy towards any behaviour on-board affecting the safety and welfare of our crew and customers.
"We'd like to thank those on board for the patience during the delay to their flight to Turkey."
An air passenger has been arrested on suspicion of being drunk on an aircraft after a flight from Glasgow to Turkey was diverted to Gatwick Airport.