The carrier's Edinburgh-based parent company, The Globespan Group, went into administration with the loss of 800 jobs.
All flights were cancelled without warning, leaving thousands of travellers stranded abroad.
Around 5,000 passengers had booked to travel with Flyglobespan over the next few days.
The airline operated flights from Edinburgh, Glasgow and Aberdeen, as well as transatlantic flights from other UK hubs including Manchester, Gatwick and Belfast.
The Department of Transport has been working with the Civil Aviation Authority (CAA) and low-cost airlines to try to bring stranded travellers home at a minimum cost.
Transport Minister Paul Clark said: "I urge all affected passengers to identify themselves as former Flyglobespan customers to alternative carriers in order to ensure they benefit from special repatriation fares.
"My principal concern is to ensure that those who are currently abroad are able to get home for Christmas."
Last night's announcement came from administrators PricewaterhouseCoopers (PWC) who said the firm had collapsed after failing to secure extra funds which it had been seeking.
They attributed the cashflow crisis to a lack of confidence in the sector following the demise of other airlines.
The group's tour operator division Globespan also folded, affecting an estimated 1,100 package holiday customers currently in Egypt and the Mediterranean and a further 27,000 with future bookings, the CAA said.
Package customers are protected under the CCA's Air Travel Organisers' Licensing (Atol) scheme but airlines are not included in the arrangement.
So while those Globespan customers will get a refund and their flight home organised for them, people who booked directly with Flyglobespan are likely to have to meet the costs of travelling home themselves.
They include an estimated 3,400 holidaymakers in Spain, Portugal, Cyprus and Egypt, according to the CAA.
Travellers booked on cancelled flights were advised not to go to the airport and contact the Globespan helpline or check its website for information.
Rival airlines easyJet and Ryanair offered passengers affected special "rescue" fares to allow them to return home where their routes overlap with those of Flyglobespan.
Thomas Cook said it had arranged additional capacity for its flights out of Glasgow Airport and Virgin Atlantic said it would be running up to seven extra flights from Glasgow to Florida in the summer.
The Scottish Government said the collapse of the airline was "extremely disappointing news" and said it would support those who have lost their jobs.
A spokesman said: "We recognise that this will be an anxious time for employees and their families, particularly at this time of year.
"The Scottish Government stands ready to offer support through the work of the Partnership Action for Continuing Employment initiative, should that be required."
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