The plane "had a technical failure at 15:40 (1840 GMT) and crashed... in an area of operations" in Yemen, Turki al- Maliki, the spokesman for the Saudi-led coalition, told AFP.
Yemen lies beside the southern mouth of the Red Sea, one of the most important trade routes in the world for oil tankers, which pass near Yemen's shores while heading from the Middle East through the Suez Canal to Europe.
"If the aggressors keep pushing toward Hodeidah and if the political solution hits wall, there are some strategic choices that will be taken as a no return point, including blocking the global navigation in the Red Sea", Houthis' Ansarullah political council chief, Saleh al-Samad, was quoted saying.
The new missile would have shotdown Tornado combat aircraft of Saudi-led coalition while it was flying over Saada province and hit another enemy F-15 plane over the capital Sanaa.
Saudi Arabia and the United States have long accused Iran of arming the Houthis in Yemen, the Arab world's most impoverished country.
The Yemen war has killed more than 10,000 people and ruined the economy and pushed the country to the verge of starvation.
Tariq Saleh, nephew of Yemen's slain former President Ali Abdullah Saleh, showed up on Thursday in the city of Ataq in Yemen's central Shabwa province, belying reports that he had been killed last month, according to a Yemeni government source.
It provided no further details and there was no immediate comment from the Saudi-led coalition, fighting the rebels since 2015, on whether the missile caused material damage or casualties. Following that outrage Houthi's can not claim a national mantle.