“A terrorist attack by the Houthi militia targeted Abha airport, killing a Syrian resident and wounding 21 civilians,” the coalition said in a statement carried on Saudi state television.
It did not confirm an attack on Jizan airport.
Saudi-owned Al Arabiya TV said a suspected drone hit the parking lot in Abha airport, which is about 200 km (125 miles) north of the Yemen border and serves domestic and regional routes.
Saudi state TV said flights had resumed at the airport, where operations were now running normally.
Earlier this month, a Houthi missile hit Abha airport in a strike that wounded 26 people.
The coalition led by Saudi Arabia and the United Arab Emirates intervened in Yemen in 2015 to try to restore the internationally recognized government that was ousted from power in Sanaa by the Houthis in late 2014.