While most nations prohibit drones from flying in pathways reserved for airliners, the millions of small consumer devices that have been purchased around the world can't be tracked on radar, making it hard for the authorities to enforce the rules.
Gatwick announced that the runway had reopened at about 3am on Thursday - but just 45 minutes later it was shut again.
Some passengers tweeted that they were stuck on planes at Gatwick while others said they were diverted to Heathrow and Manchester.
Gatwick normally operates a limited number of flights overnight.
Gatwick's statement did not provide an estimate for the resumption of flights.
All inbound and outbound flights at London's Gatwick airport have been suspended after drones were seen in its airspace, airport authorities have confirmed.
Police and aviation authorities were still investigating early on Thursday as incoming flights were diverted to other locations in the United Kingdom and nearby countries.More news: Banks Calls Trump's Demand For Border Wall Funding A "Reasonable Request"
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A spokesman apologised for any inconvenience and said Sussex Police was working alongside Gatwick staff to investigate the drone sightings.
It is unclear when flights will be allowed to leave or arrive at Gatwick today.
Chris Woodroofe, Gatwick's chief operating officer, said drones had been spotted over the airport as late as 7am on Thursday.
British Airways (BA) told one customer who complained via Twitter, that Gatwick had "stopped all arrivals and departures due to a drone".
"We have had to suspend flights while this is investigated", the airport management said on Twitter.
He criticised the "irresponsible" act and 10,000 people had been affected by the closure, including 2,000 whose flights had been unable to take off.