The attack was carried out by a Qasef-2K combat drone on Tuesday, causing a fire at the airport, according to al-Masirah TV channel.
The Saudi-led coalition did not confirm the attack, claiming that a civilian facility in Najran had been targeted with an explosive-laden drone.
On Sunday, Ansarullah warned that earlier strikes targeting an oil pipeline that runs across Saudi Arabia were the start of operations against 300 vital targets in the kingdom, the United Arab Emirates and Yemen.
Yemen’s defenseless people have been under massive attacks by a Saudi-led coalition for more than four years but Riyadh has reached none of its objectives in Yemen so far.
Since March 2015, Saudi Arabia and some of its Arab allies have been carrying out deadly airstrikes against the Houthi Ansarullah movement in an attempt to restore power to fugitive former president Abd Rabbuh Mansour Hadi, a close ally of Riyadh.
According to a recent UN report, the combined death toll from the Saudi-led aggression and disease is 233,000, or 0.8 percent of Yemen's 30 million-strong population.