The airport said it was investigating the incident and apologised to customers for the inconvenience after the runway was closed.
Early morning services between Jersey and Gatwick have been affected, but passengers are being advised to check in as normal.
A statement said: ‘Following reports of two drones flying over the Gatwick Airport airfield, we have had to suspend flights while this is investigated.
‘We apologise to any affected passengers for this inconvenience but the safety is our foremost priority.’
Gatwick advised anyone flying from the airport, or collecting someone, to check the status of their flight.
Responding to a passenger who complained their plane had been diverted to Stansted, and then Heathrow, British Airways tweeted: ‘Gatwick have stopped all arrivals and departures due to a drone, we’ve been told. Something that’s not within our control. We hope the crew keeps you updated.’
Several passengers reported long waits for take off or diversions.
Twitter user Seun Olayanju posted: ‘@AerLingus currently stuck at Gatwick waiting for the heavily delayed E10249 to Dublin. Please can you confirm if the flight will run tonight?’