The airport, which is one of the world’s busiest, has been the site of daily protests since Friday.
Videos on social media show passengers struggling to get through demonstrators, who have been sitting inside blocking departures.
The city’s leader, Carrie Lam, earlier issued a fresh warning to protesters.
Ms Lam said Hong Kong had “reached [a] dangerous situation” and that violence during protests would push it “down a path of no return”.
Mass unrest has rocked Hong Kong for 10 weeks and shows no signs of abating.
What is happening at airport?
Despite the latest warnings from officials, crowds gathered at the airport again on Tuesday.
Images from inside appeared to show protesters using luggage trolleys to build barriers and some travellers becoming distressed and angered at the disruption.
Hong Kong airport officials then announced that all check-ins were suspended from 16:30 local time (10:30 GMT).
In a statement on the airport’s website, passengers were advised to leave the terminal buildings “as soon as possible”.
It is unclear to what extent arrivals on Tuesday will be impacted.
Monday’s disruption had already led to hundreds of flight cancellations at the airport – one of the busiest international transport hubs.
Some airlines, including flagship airline Cathay Pacific, cancelled dozens of flights on Tuesday before the latest closures were announced.
Some protesters held signs apologising to passengers for the inconvenience caused by their demonstrations. Others wore eye bandages in solidarity with an injured protester and brandished slogans criticising the police’s deepening crackdown.
Doctors at Hong Kong’s Queen Elizabeth Hospital also staged a small sit-in protest opposing police violence on Tuesday, local media report.
Protests started in June in response to a proposed extradition bill, which has now been suspended, but have evolved into a more demanding pro-democracy movement.
Protests are fuelled by fear that the freedoms Hong Kong enjoys as a special administrative region of China are being eroded.
What do officials say?
On Tuesday the UN High Commissioner for Human Rights, Michelle Bachelet, urged authorities to exercise restraint during protests – amid criticism of the police response.
“Officials can be seen firing tear gas canisters into crowded, enclosed areas and directly at individual protesters on multiple occasions, creating a considerable risk of death or serious injury,” she said in a statement that called for an investigation.
The comments come after ugly footage emerged of confrontations on Sunday. A number of people, including a police officer, were injured in the clashes.
Chief Executive Carrie Lam addressed the latest violence at a hostile press conference on Tuesday.
“Take a minute to think, look at our city, our home – do you all really want to see it pushed into an abyss?” she said, at times appearing close to tears.
Her comments echoed similar remarks by an official from the Chinese Liaison Office in Hong Kong, who on Monday said the city would slide “into a bottomless abyss if the terror atrocities are allowed to continue”.