The Houthi drones targeted the fuelling station and the control tower at the airport, according to media reports.
Saudi Arabian authorities have not commented on reports of the drone attack.
On 1 August, the movement reportedly attacked a military parade in Aden, the seat of government and a stronghold of the Saudi-led military coalition, killing 36 people, according to the interior ministry. The Houthis though didn't claim responsibility for the incident.
In recent months, the Houthi movement has constantly targeted military and civilian targets across the border in Saudi Arabia.
In turn, the coalition led by Riyadh has continued to launch airstrikes against Houthis in Yemen.
According to the UN, the war in Yemen has caused a huge humanitarian crisis that has claimed the lives of at least 60,000 people.