The airline, which operates 17 aircraft on routes to 25 European cities, said it had been affected by recent rises in fuel and carbon costs and "uncertainty created by the Brexit process".
A spokesperson for Flybmi, which employs 376 staff, said: “It is with a heavy heart that we have made this unavoidable announcement today.
"The airline has faced several difficulties, including recent spikes in fuel and carbon costs, the latter arising from the EU’s recent decision to exclude UK airlines from full participation in the Emissions Trading Scheme.
"These issues have undermined efforts to move the airline into profit. 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.
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"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. We sincerely regret that this course of action has become the only option open to us, but the challenges, particularly those created by Brexit, have proven to be insurmountable.
“Our employees have worked extremely hard over the last few years and we would like to thank them for their dedication to the company, as well as all our loyal customers who have flown with us over the last six years.”
The airline is advising customers who have booked flights directly with flybmi to contact their card issuer to obtain a refund.
Anyone who has booked via a travel agent or one of flybmi’s partner airlines should contact them for details of the options available to them.
Customers with travel insurance should contact their provider to see if they are eligible to claim for cancelled flights.
Brian Strutton, General Secretary of The British Airline Pilots Association (BALPA), said: "The collapse of Flybmi is devastating news for all employees. Regrettably BALPA had no warning or any information from the company at all.
"Our immediate steps will be to support Flybmi pilots and explore with the directors and administrators whether their jobs can be saved.”