The company said its flight schedule would continue to operate as planned, while administrators examine whether the firm can be turned around.
Alitalia has received more than 7bn euros (£5.9bn) from the Italian state over the last decade.
But without further support, it may end up permanently grounded.
Last week, airline employees voted against a plan to cut jobs and salaries that would have allowed it to secure new funds.
Alitalia said in a statement that Italian shareholders and Etihad, the Abu Dhabi airline that owns 49% of Alitalia, had been "committed to recapitalise and finance the plan with 2bn euros", but that without the approval of workers, it could not go ahead.
Leave to fail
Rome has given Alitalia a 400m-euro bridging loan to allow it to keep operating during the bankruptcy process.
But Italy's finance minister has ruled out renationalising, or providing further funds for, the troubled carrier.
And public opinion seems to be behind the decision. Italians have taken to social media in recent days calling for politicians to resist bailing the airline out again. An opinion poll published on Friday suggested 77% of Italians believe the airline should be left to fail.
However, with an election looming next year, politicians may be reluctant to see Alitalia's 12,500 employees lose their jobs.
Alitalia's board said that because of "the serious economic and financial situation of the company, of the unavailability of the shareholders to refinance, and of the impossibility to find in a short period of time an alternative", they had decided to proceed with the filing for extraordinary administration.