A senior executive from the airline, Philokypros Roussounides, told The Associated Press said passengers were eligible for full refunds whether they paid by credit card or made arrangements through travel agencies.
It is the latest budget carrier to run into difficulties after Denmark's Primera Air ceased trading earlier this month.
It announced it was suspending operations and cancelling all its flights just before midnight on Wednesday (October 17).
Cobalt Air began flying in 2016 in the wake of the collapse of national carrier Cyprus Airways.
A statement on its website advised passengers not to go to airports as "no Cobalt flights will operate and no Cobalt staff will be present".
If your travel agent holds an Air Travel Organisers' Licence (ATOL), you're protected against airline failure (Photo: Getty)I'm due to fly with Cobalt.
The couple jetted out to Cyprus last week to start preparing for their October 23 ceremony - but have been left in tears after finding out their guests' flights were canceled.
Larnaca-based low-priced airline Cobalt has cancelled all flights from just before midnight Wednesday, according to a statement on its website.
Oil Rises To Approximately $80
The country made the decision to cut its oil imports long before USA sanctions against Iran take effect in November 4. This week, data from the EIA showed that the inventories had climbed to more than 9.5 million barrels.
Nine flights had been scheduled to arrive and nine to depart from Larnaca airport on Thursday.
"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".
She said that Cobalt, in search of investors, now had four days in which to submit its financial balance sheet.
Reportedly, the company has only 15 million euros in its accounts, which it needed to pay its 200 staff.
According to the airport authorities, passengers informed of the cancellation of their flight have preferred not to go to the place, which has avoided a movement of panic in the terminal.
It was not immediately clear what would happen with passengers with future bookings.
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.
The largest shareholder of Cobalt Air is AJ Cyprus, to the tune of 49%, which is owned by the Chinese Avic Joy Air.