The British Airways flight to Mauritius on Thursday was delayed and the pilot replaced, BA said.
An airline source told The Sun: “Cops rushed on to the plane and headed straight for the cockpit. The first officer was cuffed and led away.”
A 49-year-old man from west London has been arrested and remains in police custody, Sussex Police said.
The man, from Harmondsworth, West Drayton, has been arrested on suspicion of performing an aviation function when the level of alcohol was over the prescribed limit.
A spokesman for British Airways told the BBC: “We are taking this matter extremely seriously.
“We are sorry for the delay to our customers. The aircraft remained at the gate until an alternative third pilot joined the flight crew.”
The Boeing 777 was due to leave Gatwick’s South Terminal at 20:20 GMT but was delayed until just before 23:00.