The decision was taken "unanimously", the carrier said, but in a separate statement Qatar Airways, which holds a 49% stake, said it would have been ready to support the relaunch and growth of the airline.
"Qatar Airways was ready once again to play its part in supporting the growth of the airline, but this would only have been possible with the commitment of all shareholders," Qatar said.
Formerly known as Meridiana, Air Italy is the country's second-largest airline, behind Alitalia. Regional carrier Alisarda, controlled by the Aga Khan, owns the remaining 51%.
Under current rules, foreign investors cannot own more than 49% of a European airline.
After heavily investing in Meridiana, the Aga Khan was not ready to inject any further money in Air Italy, Italian daily la Repubblica reported. The Aga Khan's representative was not immediately available to comment.
Qatar Airways, which also has stakes in other international carriers including China Southern and Cathay Pacific, acquired its holding in loss-making Air Italy in 2017 and rebranded it, transforming it into a long-haul airline.
Last year, Air Italy said it expected to be profitable "soon" even though the airline also said it had been hurt by the grounding of Boeing's troubled 737 MAX.
The Sardinia-based airline had launched a five-year business plan which aimed at reaching 10 million passengers by 2022, from the 2.4 million carried so far.
But the airline's expansion came under scrutiny in Washington, where lawmakers said its U.S. routes flouted a deal between the largest U.S carriers and Gulf airlines not to add new flights to the U.S. domestic market.
Under the liquidation process - legally different from a bankruptcy - suppliers and staff will be paid off, with no outstanding debt left at the end of the process.
Air Italy said that flights would continue until Feb. 25 while flights booked for later dates would be reimbursed or re-booked on to other carriers.
Earlier on Tuesday, Italy's transport minister Paola De Micheli had called on the airline to hold back from taking any decision before meeting government ministers.
Rome is already grappling with a prolonged crisis over Alitalia, which has been through two previous unsuccessful rescues and is now being managed by a state-appointed administrator as the government seeks investors to relaunch it.
Independent aviation consultant John Strickland said the Italian domestic market was very competitive and dominated by low-cost carriers.
"Alitalia is being kept alive politically so that doesn't make life easy for other airlines. There is quite significant long-haul competition especially to the U.S.,” he said.
(Reporting by Francesca Landini and Giulia Segreti.; Additional reporting by Alexander Cornwell in Dubai; Editing by Jane Merriman)