The coordinated strike, which began at 12: 00 am, involves hundreds of airport and air traffic control staff.
The cause of the strike, which has already grounded around 300 flights, is disputes over pay and working conditions, with Milan and Rome airports expected to be the worst affected.
While most of the disruption will take place on Tuesday, some flights scheduled for Wednesday morning will also be affected.
Flights on Tuesday will operate as scheduled during peak times between 7:00 am and 10:00 am and from 6:00 pm to 9:00 pm, while larger aircraft are being deployed on busy routes to carry extra passengers, Alitalia said in a press release.
“Alitalia has taken special measures to mitigate customer inconvenience by operating bigger aircraft on domestic and international routes,” the airline said.
Alitalia passengers affected by the disruption between May 20 and 22 are entitled to rebook at no extra cost or, if their flight is cancelled or delayed more than five hours, to claim a full refund by May 28, 2019.
The strike will also affect the airlines Blue Panorama and Blue Air.
Passengers are advised to check with their airline or travel agent before setting off for the airport.