The statement by the Houthi-run Defence Ministry is a rare admission of the group's casualties.
The coalition has carried out near-daily strikes since October with claims of high tolls each time.
Capitol Hill has criticised Riyadh's involvement in the Yemen war, which is considered one of the world's worst humanitarian disasters leading US lawmakers to block military sales to the kingdom.
Yemeni officials says two ballistic missiles were used in the attack targeting a mosque and a religious school in the oil-rich Marib province.
The attack came as the Saudi-led coalition announced that it has killed 95 Houthi rebels in an operation near Marib.
Some 1,300 Houthis have been killed in 10 consecutive days of bombardment by the Saudi-led coalition, which is fighting to keep the government bastion from falling to rebel hands.
No human casualties were reported, but the Foreign Ministry’s statement said the attack caused “huge destruction” to the port’s infrastructure and burned the storehouses of some aid agencies.
US redeployment of its missile defences from Prince Sultan Air Base outside of Riyadh came as America's Gulf Arab allies nervously watched the chaotic withdrawal of US troops from Afghanistan.
At least eight people are injured in the attack on Saudi Arabia's southwestern Abha international airport, according to coalition forces.
Entisar al Hammadi tried to commit suicide "due to the decision of the central prison administration to transfer her to the prison’s prostitution section", Gulf Centre for Human Rights says, citing "reliable sources".
Information minister has written in a Twitter post that the Houthis fired two ballistic missiles and two armed drones and had hit a mosque, a commercial centre and a women's correctional facility as well as ambulances rushing to the scene.
Meanwhile, Yemen's Houthi rebels said they had attacked and hit a military air base in southern Saudi Arabia with a drone, but the Saudi-led coalition fighting the group said it had intercepted and destroyed an armed drone fired into the kingdom.
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