The airline confirmed the news in a statement posted on its website on Wednesday evening (October 17).
Passengers are advised not to attempt to travel with the airline and to contact their card provider or travel agent for a refund.
It comes the same month Primera Air collapsed into administration, leaving thousands of passengers around the world stranded.
The Cobalt statement read: "Cobalt regrets to announce that it will be cancelling all flights as of 11.50pm on October 17, 2018, due to indefinite suspension of Cobalt’s operations.
"As a result, future flights or services provided by Cobalt will be cancelled and will no longer operate.
"Passengers who have un-flown tickets are instructed not to go to Larnaca Airport or any departure airport tomorrow (October 18) as no Cobalt flights will operate and no Cobalt staff will be present.
"For refunds, please contact your credit card provider or travel agent.
"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."