The vessel, carrying shells and rockets, was intercepted 241km (150 miles) south-east of the Omani port of Salalah on Saturday, a statement said.
Its 14 Iranian crew members were detained, the statement added.
Saudi Arabia and its allies accuse Iran of providing military support to the Houthis - something it denies.
The weapons found on the fishing boat were listed by the coalition as 18 anti-armour Concourse shells, 54 anti-tank BGM17 shells, 15 shell battery kits, four firing guidance systems, five binocular batteries, three launchers, one launcher holder and three batteries.
Iranian officials have so far not commented on the report.
On Tuesday, Yemen's President Abdrabbuh Mansour Hadi told the UN General Assembly that Iran "would like to see the destruction of the country".
But a senior Iranian foreign ministry official told the Reuters news agency: "Iran has never interfered in any country's state matters and will never do it. We support peace and stability in the region."
Mr Hadi also thanked Saudi Arabia's King Salman for his "utter determination" in pursuing a military campaign to defeat the rebels and restore his government.
The coalition launched air strikes in Yemen six months ago, after Mr Hadi was forced to flee abroad when the rebels advanced on the second city of Aden.
Last week, the president returned to Aden, where his government has set up a temporary base as southern militiamen and coalition forces press northwards towards the rebel-held capital, Sanaa.
The UN says some 5,000 people, including 2,355 civilians, have been killed in air strikes and fighting on the ground since 26 March.
The coalition's blockade of Yemen's air and seaports has also greatly exacerbated the "extremely dire" humanitarian situation in the country, according to the UN.
Some 21 million people, or 80% of the population, now require some form of humanitarian assistance and almost 1.5 million people are internally displaced.
The Saudi-led coalition battling Houthi rebels in Yemen says it has seized an Iranian fishing boat loaded with weapons for them in the Arabian Sea.