A military source, speaking on condition of anonymity, told Yemen's Arabic-language al-Masirah television network that the Qaher 2-M (Subduer 2-M) missile struck the base in the far-off areas of the region, located 966 kilometers (600 miles) south of the Saudi capital, Riyadh, on Sunday afternoon.
The Houthi insurgents, who are supported by Iran, Saudi Arabia's regional rival, have given no indication that they are prepared to negotiate an end to the conflict.
Hodeidah is home to the impoverished country's biggest port from where most of the humanitarian aid reaches millions of civilians on the brink of starvation.
Saudi Arabia and the United Arab Emirates (UAE) intervened in a civil war in Yemen in 2015 against the Houthis to restore the internationally recognized government of President Abdrabbuh Mansur Hadi. The kingdom has imposed a naval and air blockade on Yemen, the poorest country on the Arabian peninsula. Since then, the alliance, which is supported by the US military, has conducted thousands of air strikes targeting Houthi fighters.
Last week, on the third anniversary of the Saudi-led bombing campaign, the Houthis fired seven missiles into Saudi Arabia, the single-biggest barrage they had ever undertaken, in what they called a justified response to Saudi bombardments.
A coalition spokesman said it was "reserving the right" to respond against Iran at an "appropriate" time.
It's the main distribution point for aid for the millions of civilians on the brink of starvation following the three-year conflict. Debris from the missiles fell on a home, killing one person.
When deliberately or indiscriminately directed toward populated areas or civilian objects, such attacks violate the laws of war.
But independent United Nations experts concluded in January that Iran had manufactured the missiles used in a series of similar missile attacks by the Houthis previous year and Tehran violated the arms embargo because it failed to prevent those missiles from getting into Houthi hands.