The attack came after Saudi Arabia's air defence forces had intercepted two drones launched by insurgents from the Ansar Allah movement, part of the Houthis, on its military air base on the country's southern border.
The UN says at least 7,000 civilians have been killed and 11,000 injured in the fighting, with 65% of the deaths attributed to air strikes by the Saudi-led coalition.
"Targeting Abha airport proves that the Houthis have obtained advanced weapons from Iran", the coalition statement said, saying the attack could amount to a war crime.
Col. Malki stressed that in the face of the Houthi militias' terrorist attacks as well as their violations, the Command of Joint Forces of the Coalition will take urgent and timely measures to deter the terrorist militias and ensure the protection of civilians and civilian objects. While President Donald Trump says he wants to talk to Tehran, the U.S. has piled on sanctions that have seen Iran's rial currency plummet along with its crucial oil exports.More news: What Falcons' coach, players said after 3-0 loss to Norway
The first Japanese prime minister to visit Iran in 41 years, Abe is expected to arrive in Tehran at around 1 p.m. and go straight into talks with President Hassan Rouhani.
A Houthi military spokesman on Tuesday threatened that the group would target every airport in Saudi Arabia and that the coming days would reveal "big surprises".
The alliance led by Saudi Arabia and the United Arab Emirates intervened in Yemen in 2015 to try to restore the internationally recognised government that was ousted from power in the capital Sanaa by the Houthis in late 2014.
Houthi-backed Al Masirah TV made the announcement and claimed the rebels had targeted the airport with a cruise missile.
Indian Express noted that Japan is traditionally a major customer for Iranian oil and has pursued mostly commercial interests in the Middle East since World War II, giving it a greater presumption of neutrality than most other close USA allies.More news: US Women Beat Thailand 13-0 In World Cup Competition
The Houthi group last month stepped up its attacks following a lull past year ahead of United Nations -led peace efforts.
May 2018 - U.S President Donald Trump pulls US out of Iran nuclear deal.
The attack on Wednesday comes as Japan's prime minister is expected in Iran to mediate between Tehran and Washington amid escalating tensions in the Persian Gulf regions.
Japan had relied heavily on Iranian oil, but has cut imports to comply with USA sanctions.More news: Trump wants more from Mexico to halt trade tariffs