The British company, which flew 17 regional jet aircraft on routes to 25 European cities, says Brexit has been a major factor in its demise.
A total of 376 people based in the UK, Germany, Sweden and Belgium worked for the airline, and their jobs are now at risk.
Thousands of holidaymakers have had their plans thrown into disarray - with the airline taking down its full website and replacing it with a statement. In 2018, Flybmi had carried 522,000 passengers on 29,000 flights.
Those affected are being told not to come to the airport unless they have rebooked flights with alternative providers. Flybmi has said it is not able to purchase, rearrange or reschedule journeys for its customers.
Richard Edwards, another disgruntled passenger, claimed he and his family only learned that their flight was cancelled after they had gone through security - and that was after their departing airport had changed from Bristol to Southampton.
Meanwhile, the airline was described as an "absolute joke" by Laura Mason, who found out she was unable to check in for a Flybmi flight that was due to depart on Sunday - a flight she had booked more than a year in advance.
British Midland Regional Limited, which ran the East Midlands-based airline, said "several difficulties" were to blame for its demise - with issues including a rise in fuel costs "undermining efforts to move the airline into profit".
A statement added: "Current trading and future prospects have also been seriously affected by the uncertainty created by the Brexit process, which has led to our inability to secure valuable flying contracts in Europe and lack of confidence around bmi's ability to continue flying between destinations in Europe.
"Additionally, our situation mirrors wider difficulties in the regional airline industry which have been well documented.
"Against this background, it has become impossible for the airline's shareholders to continue their extensive programme of funding into the business, despite investment totalling over £40m in the last six years."
The company said it sincerely regretted its decision to begin administration proceedings - but said it had become "the only option open to us" because of the "insurmountable" hurdles Brexit has created.
UK airports served by Flybmi flights included Aberdeen, Bristol, London Stansted and Newcastle - while international destinations included Frankfurt, Hamburg, Munich, Milan Bergamo, Oslo, Stavanger and Paris Charles de Gaulle.
City of Derry airport in Northern Ireland has been hard hit by Flybmi's collapse, as it has lost its only connection to London Stansted.
Last year, council officials had warned that the airport would not be sustainable without the subsidised route - and now, the terminal says it is "reviewing options for resuming the service with another airline as soon as possible".
Simon Calder, travel editor at The Independent, told Sky News: "This is I'm afraid a very, very bad sign for smaller airlines - many of which are struggling.
"And, unfortunately, it's terrible news for 400 employees as well as thousands of people who are either stranded where they don't need to be and need to get home, or indeed have bookings for future reservations.
"It's very worrying news for passengers who will now be scrambling around trying to get refunds from their credit card companies and facing much higher fares on replacement flights.
"Of course, it's very difficult finding exact replacements because Flybmi was, on many routes, the only airline."
Flybmi was born out of the ashes of British Midland - and Mr Calder said the regional arm had been struggling ever since British Airways snapped up its slots at London's Heathrow Airport.
Mr Calder said he expects many airlines will offer rescue fares to affected passengers - giving them the opportunity to purchase cut-price deals to take them to alternative airports.
British Airline Pilots' Association general secretary Brian Strutton said: "The collapse of Flybmi is devastating news for all employees.
"Regrettably Balpa had no warning or any information from the company at all."
What should customers do?
:: Do not come to the airport unless you have rebooked a flight with an alternative airline - Flybmi will not be purchasing, rearranging or rescheduling flights;
:: Customers who booked directly with Flybmi should contact their payment card issuer to obtain a refund for flights which have not yet taken place;
:: Anyone who has booked Flybmi flights via a travel agent or one of Flybmi's codeshare partner airlines should contact their agent or airline for details of options available to them;
:: Those with travel insurance should contact their provider to find out if they are eligible to claim for cancelled flights and the procedure for doing so;
:: Passengers whose flights are part of a package holiday should contact the travel company they booked with. If the firm holds an ATOL licence, it is responsible for making alternative flight arrangements or providing a full refund.
Have you been affected by Flybmi's collapse? Contact us:
:: Email - firstname.lastname@example.org
:: WhatsApp - 07583 000853
:: Your Report on Sky News apps