According to their statement via Masirah TV, the Houthis attacked the Abha Regional Airport in southern Saudi Arabia using their armed drones.
There was no mention of the attack in Saudi Arabia’s official media and Saudi officials could not immediately be reached for comment.
The Houthis, who control the Yemeni capital Sanaa and most of its populous areas, have stepped up attacks against targets in Saudi Arabia in recent months. In response, a Saudi-led coalition fighting against the Houthis has targeted military sites belonging to the group, especially around Sanaa.
The attacks are complicating U.N.-led peace efforts.
The Western-backed Sunni Muslim coalition led by Saudi Arabia and the UAE intervened in Yemen in 2015 to try to restore a Yemeni government ousted from power in Sanaa by the Houthis.
The war has killed tens of thousands of people and pushed millions to the brink of famine.
In the past week, violence has flared in the southern port city of Aden between government forces based there and southern separatists who had been fighting alongside them against the Houthis.