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.
Cobalt's grounding comes just two weeks after Latvia-based Primera Air filed for bankruptcy and a month since Belgian airline Skyworks took the same course.
Cypriot airline Cobalt has announced that it is cancelling all its flights and indefinitely suspending operations.
Cobalt started operations in 2016 and meant to fill the void left by Cyprus Airways at Larnaca and quickly rose to become the second largest airline at Larnaca Airport.
Cobalt, the largest Cypriot airline since the collapse of the state-owned flag carrier, ceased operations after reports that it had failed to reach a deal with a potential European investor.
"As a result, future flights or services provided by Cobalt will be cancelled and will no longer operate", the airline said in a statement.
The Cypriot national carrier, which flew to 23 destinations and operated flights at Gatwick, Heathrow, Manchester and Stansted, has advised customers not to travel to the airport.
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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.
'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'.
"This is an enormous disappointment after the incredible hard work and dedication put into building the airline", Cobalt said.
According to the Economy Today website, the company has only €15 million its accounts, which is expected to be used to pay Cobalt employees.
"In order to benefit (from) these fares, please bring your original Cobalt reservation when you travel".
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 Cyprus Mail said the airline's main backer is China's Avic Joy Air.