The Canadian-based start-up SkyGreece said it must "temporarily cease all operations" Thursday evening after the discount airline cancelled its fourth flight this week.
The company said it expects to resume operations "soon" but did not provide a specific date.
Meanwhile, hundreds of travellers remain stranded due to the string of cancellations.
"SkyGreece Airlines would like to apologize to all of its passengers who have been affected as a result of the company's current operational crisis," the company said in a statement. "The founders, managers and employees of SkyGreece care deeply about their passengers and have been working around the clock to resolve the problem."
The troubled airline said passengers stranded in Greece, Croatia and Canada are encouraged to contact their travel agents to arrange alternative flight plans.
Earlier on Thursday, the airline cancelled a flight from Toronto's Pearson International Airport to Greece.
A spokesperson for Transport Minister Lisa Raitt issued a statement saying Ottawa was "aware of the long delay experienced" by passengers of the cancelled flight.
"Please be assured that our government expects consumers to be treated fairly by air carriers, and a process is in place for the impartial investigation of concerns," Mark Bonokoski said in a statement.
He recommended passengers write directly to SkyGreece about their concerns, and if they are not satisfied by the air carrier's response, they can contact the Canadian Transportation Agency at 1-888-222-2592.
Thursday's cancellation comes just one day after SkyGreece cancelled three flights to and from the Toronto hub on Wednesday.
The start-up has only one plane, based in Toronto, and leases a second based in New York. The airline has been in operation for approximately one year.
One of those planes has been grounded at Pearson for the last couple of days.
According to SkyGreece, they are facing a "system-wide, multi-day delay" as a result of recent technical issues. The airline did not elaborate what those issues were but said they suffered "financial setbacks" shortly after launching its international service in May due to the Greek economic crisis.
The airline said there was an "immediate and dramatic reduction" in ticket sales, but company officials worked to maintain its scheduled service.
Last week, customers faced a four-day delay at Pearson.
The cancellations have meant some Canadian travellers are now stranded in Greece and Croatia unless they can book an alternative flight home.
Bessie Broussalis says her elderly father was vacationing in the Mediterranean country when he learned his flight on the troubled airline had been cancelled without a rescheduled date.
"It is a big inconvenience -- there is a lot of stress involved," the Quebec resident said Thursday. "He is elderly. He is 74-years-old. He has medication that he will run out of."
The troubles have also caused disgruntled travellers to take to social media to express their frustration, and many have turned to a Facebook group called "SkyGreece Troubles."
Comments range from questions about rescheduling to demands for the airline to sell its planes and refund customers' money. As of Thursday afternoon, the page had more than 460 members who said they are stranded in Toronto, Athens and Zagreb, Croatia.
SkyGreece has shut down its social media pages, but its website is still functioning, and advertises flights in the coming days. The next flight from Toronto is scheduled to leave Saturday at 4:30 p.m., but the website says no seats are available.
According to the owner of a travel agency that sold some of the SkyGreece tickets, the last two days have been "very hectic" for his clients.
"We have absolutely no clue of what's going to happen to all the passengers," SkyWay Tours Ltd. Owner Aris Sideratos said Thursday.
"I must have received over the last couple of days 30 to 40 calls from Greece...and unfortunately, we don't know what to tell them."
He said he expects to hear from SkyGreece soon so he can help his clients get home, adding that so far he's been unable to find enough space on flights to help his stranded clients. He said most flights are sold out.
Jimmy Georgiadis, a travel agent in Montreal who also sold SkyGreece tickets, advised customers to check with their travel agencies about insurance coverage.
Anyone who bought tickets using a credit card directly from the airline is advised to call their credit card company to see if they're covered.
Ontario customers can find more information about travel compensation online, through the Travel Industry Council of Ontario.
In Quebec, those who bought their tickets through a travel agency are automatically protected by a provincial fund that exists to protect travellers.
Passengers will still have to buy their return tickets, but can seek reimbursement when they return home.
With reports from CTV Toronto's Janice Golding and CTV Montreal's Stephane Giroux
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