It was not immediately clear who was behind the airstrikes but the government side blamed the UAE, which has armed and trained separatist militias in southern Yemen. Officials in the UAE declined to immediately comment.
The missile hit in the city's neighbourhood of Breiqa where a military parade was underway by forces loyal to the United Arab Emirates, a member of the Saudi-led coalition that has been fighting the Iran-backed Houthi rebels since 2015 in support of Yemen's internationally recognized government.
The spokesman of the Saudi-led coalition at war in Yemen against the rebel Houthis was quoted in the state-run Saudi Press Agency as saying the airport in Abha was struck shortly after 9 p.m. local time on Sunday.
A Saudi-led coalition launched airstrikes on Iran-allied Houthi forces in Yemen's capital Sanaa, Saudi state television reported part of an escalation of tit-for-tat strikes that has stoked regional tensions.
Mohammed Ali al-Houthi said the Iran-backed rebels ordered the cessation of rocket and drone attacks on the Saudis and forces loyal to coalition member the United Arab Emirates at the request of U.N. special envoy Martin Griffiths.
The Houthis last July unilaterally halted attacks in the Red Sea to support peace efforts, after Saudi Arabia suspended temporarily oil exports through a strategic Red Sea channel following attacks on crude tankers.
Houthis rule the most populous areas of chronically unstable Yemen, where many parties have been competing for territory and influence, from loyalists of the late President Ali Abdullah Saleh to southern separatists to al-Qaeda.
Ground troops -- which include United Arab Emirates forces, Sudanese and Yemenis drawn from various factions -- have surrounded the main airport compound but have not seized it, a Yemeni military source and residents said.
Arab warplanes and warships continued to pound Houthi positions in Yemen's Hodeida on Friday in operation “Golden Victory” to capture the strategic harbour that is the main entry point for food in Yemen.