Gatwick's runway has been shut since Wednesday night, as devices have been repeatedly flying over the airfield.
Sussex Police said it was not terror-related but a "deliberate act" of disruption, using "industrial specification" drones.
About 110,000 passengers on 760 flights were due to fly on Thursday. Disruption could last "several days".
An airline source told the BBC flights were currently cancelled until at least 19:00 GMT.
The airport advised that the runway would not open "until it was safe to do so".