Airline SAS will temporarily halt most of its flights from Monday until conditions for commercial aviation improve, it said, as demand for flights has "more or less disappeared".
Airlines worldwide are cutting flights and costs amid plunging demand and U.S. travel restrictions on European passengers during the coronavirus outbreak.
Europe's second biggest airline Lufthansa is reported to have asked for state aid, while IAG's British Airways said it was in a battle for its "survival".
SAS, part-owned by Sweden and Denmark, said on Sunday it would temporary lay off up to 10,000 employees, or 90% of the airline's total workforce.
"Demand for flights into, out of, and within Scandinavia has more or less disappeared," chief executive Rickard Gustafson told a press briefing on Sunday.
"We have to adapt to current circumstances and starting tomorrow, Monday, we will temporary pause a large part of our operations and we will heavily reduce the number of flights in our entire network," he added.
Gustafson said the company had worked in the past few years to improve the financial stability of the company.
"Obviously, an airline with no revenue does not stand up for very long, but we have built good financial preparedness and good liquidity so we will manage for a good while," he said.
Gustafson said he welcomed measures announced by the Danish government on Sunday, in which the state covers 75% of employees' salaries in embattled Danish companies if they promise not to cut staff.