Hong Kong-based carrier Cathay Pacific warned the disruption could extend into Tuesday, and advised customers to "postpone non-essential travel".
At the airport, protesters held signs reading "Hong Kong is not safe" and "Shame on police".
They accuse the force of using increasingly violent and disproportionate tactics to suppress protests.
Over the weekend police fired tear gas into subway stations and crowded shopping streets as they confronted protesters at nearly a dozen locations across the city.
Protesters responded by hurling bricks and spraying riot police with fire extinguishers and water hoses.
Demonstrators were also enraged at police apparently dressing in the black T-shirts worn by the pro-democracy movement to infiltrate the rallies and make surprise arrests.
Officials said 45 people were hurt in the clashes, including two who were in serious condition.
Among them was a woman who suffered a face injury, reportedly after being hit by a bean bag round, with rumours circulating that she had lost her vision in the incident.
Images of her lying on the ground with blood pouring from her face quickly went viral and featured on posters calling for new demonstrations, including some reading "an eye for an eye."
The expression was also spray-painted in Chinese at several places in the airport, where many demonstrators wore eye patches or bandages in solidarity with the injured woman.
"It is becoming more and more dangerous, but if we don't still come out at this point, our future will become more frightening, and we will lose our freedoms," said one 22-year-old protester who gave her family name as Chan.
It was the 10th consecutive weekend that protesters had taken to the streets in a movement that began over opposition to a bill allowing extradition to mainland China.
The protests have morphed into a broader bid to reverse a slide of democratic freedoms in the southern Chinese city.
The city's Beijing-backed leader has ruled out concessions and warned the protesters were causing economic chaos.
The city's transport chief Frank Chan said Monday that Hong Kong would pay a "heavy price" for the airport's closure.
In Beijing, authorities slammed violent protesters who threw petrol bombs at police officers, linking them to "terrorism".
"Hong Kong's radical demonstrators have repeatedly used extremely dangerous tools to attack police officers, which already constitutes a serious violent crime, and also shows the first signs of terrorism emerging," said Yang Guang, spokesman for the Hong Kong and Macao Affairs Office of the State Council.
"This wantonly tramples on Hong Kong's rule of law and social order."
The protests have infuriated Beijing, which has lashed out at Cathay Pacific, imposing new regulations on the airline that ban staff sympathetic with the demonstrations from flying to or over the mainland.
Cathay has found itself caught in the crossfire in the increasingly bitter standoff, and warned staff on Monday that they could be fired if they participated in, or supported "illegal protests".
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