The airline has a staff of about 200, and had sought to fill a gap in Cypriot air transport following the demise of Cyprus Airways in early 2015, a state-controlled carrier that dominated mainly short routes from the island.
They said Cobalt had ceased operations after failing to reach a deal with a potential European investor to help it pay for leasing its six aircraft - two Airbus 319s and four Airbus 320s.
Cypriot airline Cobalt has told passengers not to turn up for their flights.
A couple has been left nearly $5,900 out of pocket after their dream wedding in Cyprus was ruined when Cobalt Airlines folded overnight.
The Cypriot airline, which operates services from Heathrow, Stansted and Gatwick, said that all flights were being cancelled as of 11.50pm on Wednesday.
She said: "We thought it would be easier and less stress getting married overseas but it's a nightmare".
"We sincerely apologise once again and would like to thank our very loyal customers for their support over the last two years of Cobalt operations".
According to officials cited by the agency, the NAC, Cobalt Air would be in debt to the tune of tens of millions of dollars since its first commercial flight in July 2016.
The announcement of the closure of the airline has left hundreds of passengers in limbo, while nine flights of Cobalt were from Larnaca on Thursday and nine more to get there. If so, they will provide a full refund or alternative flight.
In terms of getting a new flight, Cyprus Transport Minister Vasiliki Anastasiadou has promised help will be given to those stuck in Cyprus or overseas as a result of the collapse.
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. AJ Cyprus is owned by China's AVIC Joy Air.