The coalition has been battling the rebel Houthi movement since 2015.
It intervened after the Houthis ousted the internationally-recognized government from power in the capital Sanaa.
The Houthi rebels said they used ground-to-air missiles to down the warplane on February 14. They also accused the coalition of killing 30 people in retaliatory airstrikes in al-Jawf on the next day.
Saudi Arabia has not provided details of any casualties from the crash, or what caused it.
Yemen has been at war since 2015, when President Abdrabbuh Mansour Hadi and his cabinet were forced to flee the capital Sanaa by the Houthis.
Saudi Arabia backs President Hadi, and has led a coalition of regional countries in air strikes against the rebels.
The coalition carries out air strikes almost every day, while the Houthis often fire missiles into Saudi Arabia.
Yemen civil war has triggered the world’s worst humanitarian disaster, with an estimated 80% of the population – more than 24 million people – requiring humanitarian assistance or protection. Tens of thousands of people have died n Yemen as a result of the conflict.
The Houthi-run Saba News in Yemen said the missile had been a Burkan H2.
The rebel group is believed to have access to a stockpile of Scud ballistic missiles and home-grown variants. Saudi forces have previously brought them down with Patriot surface-to-air missiles bought from the US.
In May, a day before President Donald Trump was due to arrive in Riyadh for a visit, the Houthis fired a missile towards the city, but it was shot down 120 miles from the capital.
Yemen has been devastated by a war between forces loyal to the internationally recognized government of President Abdrabbuh Mansour Hadi and those allied to the Houthi rebel movement.
Saudi Arabia is leading a campaign to defeat the Houthis, and is the biggest power in an international air coalition that has bombed the rebel group since 2015.
On November 1, a suspected strike by the Saudi-led coalition killed at least 26 people at a hotel and market in northern Yemen, medics and local officials said.
The coalition, which rights groups say has bombed schools, hospitals, markets and residential areas, said it struck a “legitimate military target”.