It flew to 23 destinations in Europe - including Heathrow, Stansted, Gatwick and Manchester in the United Kingdom - as well as Russian Federation and the Middle East.
But late on Wednesday night, its website was abruptly replaced with a single-page statement announcing the cancelation of all of its flights from 23:50 pm.
"We feel the need to help passengers who are stranded either in Cyprus or overseas and want to return to their place of residence", Transport Minister Vassiliki Anastassiadou said.
The sudden collapse comes after Danish budget carrier Primera Air ceased trading earlier this month, leaving thousands of travellers stranded overseas.
The Larnaca-based carrier warned ticketed passengers not to go to any departure airport as no flights will operate and no staff will be present.
"For refunds, please contact your credit card provider or Travel Agent".
But it was not immediately clear what would happen to stranded travellers - or customers with future bookings.
A senior executive from the airline, Philokypros Roussounides, told AP on Thursday that Cobalt's six Airbus passenger jets have been grounded.
Two travel operators on the island had been instructed to manage the repatriations and issue tickets on other airlines.
The minister confirmed the airline was struggling but had informed authorities it was looking for funding.
She said: "We thought it would be easier and less stress getting married overseas but it's a nightmare".
Cobalt started operations in 2016 after the demise of Cyprus Airways the previous year.
Other reports put the debt at around 100 million euros ($115 million).
It employs about 200 staff.
It was unable to reach a deal with "potential European investors" and is said to have missed several lease payments earlier this month.
If the company refused to speak officially on its financial position, sources within the company have attributed his problem of liquidity to the difficulties encountered by chinese investors to export their capital, due to restrictions imposed by Beijing.
The airline's largest shareholder is AJ Cyprus, with 49 percent of the shares.