Monday's demonstration marked the fourth straight day of protests at the HKIA as anti-government anger continued.
Airport staff blamed the disruption on the large crowds of protesters who had swarmed the terminal building, impeding passengers from the check-in process.
"Airport operations at Hong Kong International Airport have been seriously disrupted, all flights have been cancelled. All passengers are advised to leave the terminal buildings as soon as possible. Affected passengers please contact their respective airlines for flight arrangement," the airport said on its website.
Officials advised members of the public not to travel to the airport but said arrivals already heading into Hong Kong would still be allowed to land, but all other scheduled flights were cancelled.
Many of those protesting were critical of the actions of the police, who on Sunday were caught on film firing teargas and non-lethal ammunition at close range.
Some protesters were wearing bandages over their eyes in response to images of a woman bleeding heavily from her eye on Sunday, having reportedly been shot by a police projectile.
Demonstrators descended on the arrival and departure halls of the complex, with their growing numbers preventing passengers from checking in or clearing airport security for flights, the South China Morning Post reported.
Addressing Chinese state press and some Hong Kong media outlets, China's Hong Kong and Macau Affairs Office spokesperson Yang Guang said the protests had started to show "early signs of terrorism".
"In recent days, Hong Kong's radical protesters have repeatedly attacked the police with highly dangerous tools, which constitute serious violent crimes and have started to show signs of terrorism," he said, according to the daily.
He said China would clamp down on the unrest with an "iron fist".
The special-status Chinese territory has been gripped by 10 weeks of protest, initially over the local government's plans to approve a controversial extradition bill whose critics said would have allowed China to seek out fugitives in Hong Kong.
The now-abandoned extradition bill has morphed into a broader anti-government movement seeking to reverse a general decline in freedom.
About 75 million passengers passed through the airport which is a major international transit hub in 2018.
Meanwhile, Hong Kong flag carrier Cathay Pacific warned staff they could be fired if they "support or participate in illegal protests". The development came days after Beijing mounted pressure on the airline and a #BoycottCathayPacific campaign began to spread.
The Hong Kong police also unveiled a water cannon vehicle as a new tool to combat the protests.
On Sunday, clashes between protesters and the police escalated across districts, including Tsim Sha Tsui, Sham Shui Po, Kwai Chung and Causeway Bay.
The night ended with unprecedented scenes inside metro stations as officers unleashed tear gas inside Kwai Fong station and charged protesters inside Tai Koo station.
( With inputs from IANS )