Flights are being diverted to Vienna, Bratislava and other major airports nearby.
The airport closed at 11:50 a.m. local time and may not reopen until about 10:00 a.m. on Saturday, officials said.
Ferenc Liszt International Airport is the largest in Hungary, operating a single terminal that handles some nine million passengers a year.
The airport operator said on its website: “Currently we plan to reopen air traffic at the airport at 10:00 [local time on Saturday] but that time may still change.”
Passengers were urged not to travel to the terminal.
The airport was originally called Budapest Ferihegy International, until it was renamed after the composer Franz Liszt in March 2011.
It is partly owned by Germany’s Hochtief company.
Easyjet said on its website that all its flights scheduled to operate through Budapest on Friday had been re-scheduled to operate on Saturday and urged customers to check the new timings.
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