"Other than departure flights that have completed the check-in process and the arrival flights already heading to Hong Kong, all other flights have been cancelled for the rest of today," said airport authorities.
They will resume at 6am on Tuesday.
People are demonstrating over claims of police brutality, a planned extradition law and a call for more democracy.
The protests at the airport have not been violent but Sky's Stuart Ramsay, in Hong Kong, said the sit-in had now reached thousands and is causing "chaos".
He said numbers had increased after a paramedic was hit in the eye by a tear gas round at the weekend and she may lose her vision.
"The sit-in protest that was already under way at the airport suddenly has magnified and now we have thousands and thousands of people cramming in there," said Ramsay.
The grounded flights caused a huge traffic jam on the roads leading back to the city centre, with more protesters seen walking towards the airport.
By early evening, Ramsay said numbers had thinned out as some headed back into the city fearing the arrival of police, but others remained waiting for the final international arrivals.
Police have been firing tear gas and rubber bullets at gas mask-wearing protesters during two months of unrest on Hong Kong's streets.
Some of them have been throwing bricks and other projectiles in response.
Police stations have also been attacked and last month protesters stormed the legislative council building.
Ramsay said "snatch squads dressed in civilian clothes" were used alongside riot police during the weekend protests, as authorities took a tougher approach.
"There has been escalation in the last 24 hours from demonstrations that were broken up - in a relatively reasonable way - to very hardcore police tactics... it's heightened the tension between the two sides," said Ramsay.
"The shooting in the eye of this young lady seems to have got everyone on the streets again and now they're really focusing on the airport."
Police said they were still gathering evidence about the case of the woman hit in the eye.
They also defended firing tear gas into an underground station and deploying officers dressed as protesters.
"Our decoy officers do not take part in any unlawful activities," said deputy police commissioner Tang Ping-keung.
A statement from the government department that deals with Hong Kong has warned of "no leniency or mercy".
China's Hong Kong and Macao Affairs Office said the situation was "beginning to show the sprouts of terrorism" and is an "existential threat".
"One must take resolute action toward this violent criminality, showing no leniency or mercy," said the statement, attributed to spokesman Yang Guang.
Police also showed off water cannon on Monday that could be used to break up any more protests - something Amnesty International has warned could cause serious injuries.
Hong Kong's chief executive Carrie Lam has said plans for the extradition law are "dead" - but protesters want it formally withdrawn.
The legislation would allow people to be sent to China for trial, with activists worried critics of Beijing would be sent to the mainland and denied proper justice.
However, protesters' grievances have broadened over the past weeks to encompass a push for greater democracy and the protection of Hong Kong's "one country, two systems" model.
China has so far continued to back Carrie Lam, amid fears it could deploy soldiers based in the territory if the situation is not brought under control.
Protesters want Mrs Lam to resign and a free election to replace her.