A spokesman for the airport in Kathmandu said wildlife and security officers were searching for the animal, believed to be hiding in the drains, after it was spotted by a pilot.
"We closed the airport for about 30 minutes after the incident was reported but we haven't found the leopard yet," Prem Nath Thakur told AFP.
One international flight was delayed but no other flight was scheduled during the closure.
Kathmandu is close to forested hills and leopards are occasionally known to stray into the city.
In the past birds have posed serious safety problems at the single-runway airport, although stray cattle and dogs have also been known to disrupt flights.
In 2016, a plane with nine passengers was forced to make an emergency landing when a bird struck its right wing.
Nineteen people were killed in 2012 when an aircraft hit a bird and crashed shortly after taking off from the airport.
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