The attack in Sharurah was aimed at "weapons depots and command centres" and was carried out with rockets and drones, said Houthi spokesman Yahya Saree, according to AFP.
He has not presented any evidence or said when the attack took place.
However, intense fighting has been ongoing for several days in Yemen between the Iran-backed Houthis and Yemeni government forces supported by Saudi Arabia.
Yemen's Saudi-backed government describes the Houthis' rapid advance along the Red Sea coast as a "painful" development.
In parallel with the alleged attack on the military base, Saudi Arabia says that two people and several buildings were damaged in a Houthi attack on a community in the Saudi province of Jazan in the southwest of the country.
The statement singles out the Houthi rebels as the attackers.
The Houthi movement recently captured large parts of Yemen's Red Sea coast, consolidating its control over the Bab al-Mandab Strait, which is important for maritime traffic. On Saturday, the Yemeni government website published videos that allegedly showed counterattacks targeting the Houthis, according to Al Jazeera.
There were no Saudi statements on Sunday about new counterattacks against the Houthis.
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