The attack on Abha airport - located in the southern part of the kingdom - was launched by Yemen's Houthi rebels. The airport is located about 200 km north of the Yemen border.
"The terrorist attack resulted in martyring a Syrian national and injuring seven civilians," said Colonel Turki Al Maliki, a military spokesman, according to Gulf News. The toll of injuries later rose to 21 including four Indians, two Egyptians, 13 Saudis, and two Bangladeshis.
It was also reported that the attack had "physically damaged" one of the restaurants at the airport as well as 18 vehicles.
Saudi Arabia has been at war with the Houthis for more than four years. The recent attack is not the first to take place in the kingdom. On June 12, the Houthis targeted the same airport with a rocket, wounding 26 people at the time.
UN spokesman Farhan Haq described the stated attack as a "serious threat to regional security," according to Gulf News.
"We urge all parties to prevent any such further incidents, which risk escalating the current situation, pose a serious threat to national and regional security and undermine the UN-led political process," Haq said.
The Iran-backed Houthis also claimed responsibility for the explosive-laden drone strikes against oil facilities in the kingdom.
The attacks come amid rising tensions between Iran and Gulf Arab states allied to the United States. The more recent attack came just one day before Mike Pompeo, the American secretary of state, was set to visit Saudi Arabia to discuss the rising tensions with Iran.
On Monday, Pompeo landed in Saudi Arabia and is expected to meet with King Salman and Crown Prince Mohammed bin Salman in Jeddah. He is also expected to fly to the UAE to discuss Iran with officials there.
"We'll be talking with them about how to make sure that we are all strategically aligned and how we can build out a global coalition," Pompeo said, according to France 24.
Last week, U.S. President Donald Trump ordered a military strike on Iran after the latter shot down an unmanned U.S. drone. Trump later backtracked on his order.
"What happened is, I said, 'I'm not going to do it. I'll save it. If they do something else, it'll be double,'" Trump said in an interview on Sunday.
"I'm not looking for war and if there is, it'll be obliteration like you've never seen before."