Medics and a witness who saw the wreckage said the air strike had destroyed a house in al-Hali district, where displaced civilians from other provinces were settled.
The 12 victims were all from the same family, they said.
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A spokesman for the Saudi-led coalition told Reuters: "We take this report very seriously and it will be fully investigated as all reports of this nature are - using an internationally approved, independent process. Whilst this is ongoing, it would be inappropriate to comment further."
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 famine. The operation of port, controlled by the Iran-aligned Houthis, was not affected by the air strike.
Saudi Arabia and the United Arab Emirates intervened in a civil war in Yemen in 2015 against the Houthis to restore the internationally recognised government of President Abd-Rabbu Mansour Hadi.
The alliance, which includes other Sunni Muslim states, has conducted thousands of air strikes targeting Houthi fighters and has often hit civilian areas, although it denies ever doing so intentionally.
The war has killed more than 10,000 people, displaced more than 2 million and driven the country - already the poorest on the Arabian Peninsula - to the verge of famine.