Norwegian is cancelling about 3,000 flights until mid-June following a decline in demand from the coronavirus outbreak.
That is about 15pc of the airline’s total capacity for this period.
The company has also put several other measures in place, including temporary layoffs of a “significant share of its workforce”.
Affected customers will be informed about cancellations.
Chief executive Jacob Schram said: “Unfortunately, cancellations will affect a significant share of our colleagues at Norwegian. We have initiated formal consultations with our unions regarding temporary layoffs for flying crew members as well as employees on the ground and in the offices.”
He added: “This is a critical time for the aviation industry, including us at Norwegian. We encourage the authorities to immediately implement measures to imminently reduce the financial burden on the airlines in order to protect crucial infrastructure and jobs.”
The Telegraph reported on Sunday that Arrowstreet Capital, a $106bn (£81bn) hedge fund launched by UK-born Harvard professor John Campbell, is among investors betting Norwegian will be the next airline to fail.
Several airlines have slashed capacity to and from Italy in the wake of the nationwide lockdown announced on Monday.
Ryanair will suspend all flights until April 8, while British Airways has also stopped flying to Italy.
EasyJet continues to operate a small number of flights to the country.