Norwegian Air has cancelled 40% of its long-haul routes and a quarter of its short-haul services.
The changes apply to flights up until the end of May.
The majority of flights to the US from European cities have been pulled.
All routes between London Gatwick and the US will continue to operate as normal.
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It follows an announcement from US president Donald Trump that the UK is excluded from a transatlantic travel ban from 26 European countries.
Norwegian will cancel a large share of its domestic flights in Norway and flights within Scandinavia, such as Oslo-Copenhagen and Oslo-Stockholm. Flights to Italy will also be cancelled.
The airline has also announced temporary layoffs of up to 50% of its staff and warned the number may increase.
Chief executive of Norwegian, Jacob Schram, said: “This is an unprecedented situation and our main priority continues to be the care and safety of our customers and colleagues.
“The new restrictions imposed further pressure on an already difficult situation. We urge international governments to act now to ensure that the aviation industry can protect jobs and continue to be a vital part of the global economic recovery.”