The announcement affects several flights from Dublin and Belfast City airports to UK cities.
Belfast flights from Leeds Braford Airport are affected, but the Dublin route is not as it is operated by Ryanair.
An Aer Lingus statement said: “Late on the evening of June 11, Stobart Air notified Aer Lingus that it was terminating its franchise agreement with Aer Lingus with immediate effect.
“As a result, all Aer Lingus regional flights operated by Stobart Air are cancelled.
“Stobart Air referred to the continuing impact of the pandemic which has resulted in almost no flying since March 2020.
“Stobart Air has ceased trading and is now in the process of appointing a liquidator.
“Aer Lingus apologises to customers for the inconvenience caused by the cancellation at such short notice of all flights operated by Stobart Air.
“Aer Lingus is now communicating to customers to advise them of their options for refund or rebooking.”
Customers who have booked flights are advised not to go to the airport and to check the Aer Lingus website.
Flights from Belfast City Airport to Leeds Bradford, Manchester, Birmingham, Edinburgh, Exeter and East Midlands have been cancelled.
The announcement also affects flights from Dublin to Kerry, Donegal, Glasgow, Edinburgh and Newquay.
A spokesperson for Stobart Air said: “It is with great regret and sadness that Stobart Air can confirm that the board is in the process of appointing a liquidator to the business and the airline is to cease operations with immediate effect.
“Stobart Air apologises to all its customers for the inconvenience caused at short notice. All 480 staff at the airline have been informed.
“Last April, Stobart Air announced that a new owner had been identified. However, it has emerged that the funding to support this transaction is no longer in place and the new owner is now unable to conclude the transaction.
“Given the continued impact of the pandemic which has virtually halted air travel… and in the absence of any alternative purchasers or sources of funding, the board of Stobart Air must take the necessary, unavoidable and difficult decision to seek to appoint a liquidator.”
A Leeds Bradford Airport spokesman said: "We regret to inform our passengers of the sad news that Stobart Air has ceased trading. Aer Lingus Regional flights, operated by Stobart Air, are cancelled.
"Our advice to passengers who are due to fly is to not travel to the airport. Instead, they should visit: https://www.aerlingus.com/support/flight-disruption-information
"Aer Lingus is looking to provide flights from LBA for impacted customers over the next few days, including flights on Sunday and Monday.
"Information will be available on the above website.
"We’re very saddened to hear this news affecting our colleagues at Stobart Air and the impact to our customers.
"We are working to attract a replacement airline for our Belfast service."
Irish Transport Minister Eamon Ryan said: “The announcement is concerning news for the affected workers and for regional connectivity.
“We will be engaging with all stakeholders today and over the coming days to restore connectivity to the regional airports affected.”