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.
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 are 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.
The tensions were sparked by a now-shelved extradition bill, which has led to 10 weeks of civil unrest and escalating violence. The legislation would have allowed the transfer of fugitives to jurisdictions with which the city has no such agreement, including mainland China.
Now, the demonstrations have morphed into a broader anti-government movement seeking to reverse a general decline in freedom.
Officials advised members of the public not to travel to the airport but said arrivals already heading into Hong Kong would be allowed to land.
About 75 million passengers passed through the airport which is a major international transit hub in 2018.
This comes as clashes between protesters and the police escalated on Sunday 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 )