Low-cost airline Cobalt has cancelled all flights from midnight Wednesday according to a statement on its website.
The carrier, which has operated flights in and out of Cyprus since 2016 - including flying UK holiday-makers to the island - has suspended operations.
Local media said Cobalt had failed to reach a deal with a potential new investor.
The Cyprus Mail said the airline's main backer is China's Avic Joy Air.
The airline's statement said future flights would not operate due to "indefinite suspension of Cobalt's operations", and advised passengers not to go to the airport.
They should contact their credit card provider or travel agent instead, it added.
It is not yet clear how many passengers have been affected, but nine flights had been scheduled to arrive and nine to depart from Larnaca airport on Thursday.
It flew to 23 destinations in Europe - including Heathrow, Stansted, Gatwick and Manchester in the UK - as well as Russia and the Middle East.
Cypriot Transport Minister Vassiliki Anastassiadou said the government would pay for tickets to help travellers get back to where they started from, but stressed it would only cover return tickets.
She said telephone numbers would be announced soon to help passengers stranded either in Cyprus or overseas.
The fate of Cobalt's 200 staff is unclear.
Last year, Cobalt said it had carried 740,000 passengers in its first 16 months of operation. By contrast, Europe's biggest airline Lufthansa carried about 130 million people last year.
Before 2016, short-haul flights out of Cyprus were dominated by state-controlled Cyprus Airways. But it collapsed, which left room for the new operator.
Danish budget carrier Primera Air ceased trading earlier this month after 14 years of operation.
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