Aer Lingus chief executive Mr Willie Walsh has resigned his position along with two other prominent members of the airline's board.
Chief financial officer Mr Brian Dunne and chief operations officer Mr Seamus Kearney have also resigned, the Department of Transport confirmed this afternoon.
The three had led an unsuccessful management buy-out proposal of the airline.
The Minister for Transport, Mr Cullen, said this afternoon he regretted their decision but the development would not stand in the way of the company's plans.
He said he would meet with Aer Lingus chairman Mr John Sharman in the coming days to assess the situation.
Mr Cullen said: "The company, through the combined effort of staff, management and the board has been turned into the best-performing national airline in the world.
"However, the company does face challenges, challenges which are the same today as they were yesterday."
He said: "My desire and that of the Government to keep the airline on a sustainable growth path is undiminished by today's development. A new management team will be charged with consolidating the progress of recent years and building for the future."
It is not known why the three men resigned, but they have been widely regarded as successful in their roles. Labour Party transport spokeswoman Ms Roisín Shortall said employees and the public should be informed of reasons "for this extraordinary decision".
Fine Gael's Ms Olivia Mitchell blamed the Government's failure to clarify how the airline will raise the funding it needs to remain competitive. She described the resignations as "disastrous".
The Progressive Democrats spokesperson Mr Tom Morrissey - a long-standing critic of Government Transport policy - said the value of the company will be "slashed" by the resignations.
He also described last month's questioning of the three men before the Public Accounts Committee as a "mugging".
The Green Party's Mr Eamon Ryan said the departures could jeopardise the future of the company and said the Taoiseach, Mr Ahern, and the former transport minister, Mr Seamus Brennan bear responsibility for the company executives being "very shoddily treated".
As chief executive, Mr Walsh transformed an airline facing losses of €152 million in 2002 to one that made a profit of €69 million last year.
However, the turnaround caused considerable industrial relations tensions with 2,000 workers already laid off and a plan to shed another 1,300.