Many travellers took to Twitter to vent their frustrations, with some reporting delays of up to three hours for bags.
An airport spokesman said the delays were caused by "resourcing issues" involving the baggage handling company Swissport.
The airport later tweeted that operations were "returning to normal".
The passengers affected had flown with British Airways, Monarch, Thomas Cook and Thomson airlines.
They were told their luggage would be sent to their homes, the BBC reported.
Sian Edwards tweeted: "@swissportUK - you need to sort out Gatwick, not enough staff for a Saturday in July - shocking!"
Sue Heffernan Smith tweeted: "I landed at Gatwick at 11.20pm and have just got on a train home. It is now 4.20am. Baggage fiasco."
Will Bower tweeted: "Pulling an 'all nighter' with my 700 friends at Gatwick North Terminal Baggage Reclaim, bring water."
Using its own Twitter account, Gatwick advised many passengers to go home without their bags. It said they should arrange for bags to be sent on before leaving the airport.
"Due to resourcing issues with the baggage handlers Swissport tonight, there have been issues and delays with passengers' luggage," he said.
"Gatwick has provided extra staff to help the airlines and their baggage handlers improve their service, as well as providing welfare and water for passengers waiting in the baggage areas, but we are sorry for the delays they have faced."
Swissport has not yet responded to a request for a comment, the report said.
Earlier this month, Gatwick apologised after passengers faced delays of up to 90 minutes to reclaim their baggage, and blamed those problems on a shortage of staff at Swissport.
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