The cancellations represent 15 percent of the airline's capacity for the period.
“The past week, Norwegian has experienced reduced demand on future bookings. The company will cancel about 3,000 flights to meet the change in demand. The cancellations represent approximately 15 percent of the total capacity for the period mid-March to mid-June,” the company said in a statement to the Oslo stock exchange.
The company added that the cancellations would affect the airline's entire network.
“More details will be shared as soon as they are ready to be implemented. Affected customers will receive information about these changes as soon as they take place,” the statement continued.
A significant number of staff at the company are likely to be affected by the decision.
“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.
“We will continue to engage in constructive dialogue with unions and employees to work through this difficult situation together,” Norwegian CEO Jacob Schram said in the statement.
Norwegian has already suspended flights between Oslo and Milan until May based on travel guidelines from Norway's foreign ministry as well as health authority recommendations.
The International Air Transport Association (IATA) last week estimated that losses in revenue for airlines due to the new coronavirus could range from $63 billion (55 billion euros) to $113 billion, depending on whether the spread of the virus was contained.
Norwegian, which has been in deficit for three years and is heavily indebted due to an ambitious expansion policy, especially in long-haul flights, is particularly vulnerable.
Last Thursday, the company withdrew its 2020 forecast, which predicted a return to profits, citing the new coronavirus epidemic.
In early afternoon trading on Tuesday, shares in Norwegian were down 5.8 percent on the Oslo Stock Exchange.
Meanwhile in neighbouring Denmark, authorities on Tuesday banned all flights to heavily affected areas, such as parts of China, Iran and Italy, for two weeks.
The Danish government also urged people to avoid public transport during rush hours.
On Tuesday, Denmark had 158 confirmed cases of the new coronavirus, and Norway had 192.