The country's civil aviation authorities said one person was killed and eight wounded in an attack on King Khalid International Airport in the Saudi capital Riyadh, and two were killed and 28 wounded in an attack on facilities at Abha airport.
The Saudi airport attacks were among a series of strikes targeting aviation infrastructure.
Yemen's Houthis attacked Aden's international airport with ballistic missiles and explosive-laden drones earlier on Wednesday, the country's transport ministry said.
One missile landed near the runway at Aden International Airport minutes before a flight from Cairo was due to land, according to officials.
Authorities cancelled the landing and diverted the aircraft to Jeddah while two planes on the runway were moved away from the area over fears of further strikes, it added.
Aden International Airport is the main international gateway for parts of Yemen outside Houthi control.
Battles have focused in recent days on areas around the Bab el-Mandeb Strait, a shipping route that has become more crucial for energy exports since the conflict between the US and Iran restricted trade through the Strait of Hormuz.
This week, Yemeni government forces with Saudi-led coalition air support launched a counter-offensive to recapture strategic territory near the strait and around the town of Mocha that the Houthi rebels had captured in September but it is unclear if their advance will hold.
The fighting has revived a complex 12-year war in Yemen that led to one of the worst humanitarian crises globally and fragmented the Arab world's most impoverished country.
The number of people displaced since the latest round of fighting began has risen to more than 200,000, the International Organisation for Migration said on Wednesday.
"People are running for their lives and finding nowhere safe to go," IOM director general Amy Pope said, calling for more funding amid rising needs for food and shelter.
Both sides allege that hundreds of people have been killed in fighting, without providing details.
The United Nations says three in four families are going hungry in parts of Yemen.
The Iran-aligned Houthi rebels have repeatedly targeted infrastructure including airports, oil refineries and pipelines in Saudi Arabia.
Any Houthi stranglehold on the strait could threaten shipping or global oil flows, and Saudi Arabia has been seeking international assistance to repel the Houthi movement.
Turkey is sending mainly defensive and technical support, two officials said on Wednesday, after the NATO member and Pakistan pledged to implement a collective defence commitment under their newly formed Mecca Joint Defence Agreement pact.
Hussam Radman, a researcher at the Sanaa Center, a Yemen-focused think tank, said pro-government forces including the Giants Brigade, a conservative Sunni Salafi group that has led the counter-offensive, are trying to take control of Dhubab and to advance in the mountains to its east.
Control of those highlands would allow for government forces to more easily advance up the rest of the coast, he said.
Houthi fighters, who control much of Yemen's north, seized the capital Sanaa in 2014, prompting a military coalition led by Saudi Arabia to intervene.
A United Nations-brokered truce in 2022 largely halted heavy fighting but it did not lead to a lasting settlement.
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