A Yemeni military source told Iran's Press TV, on condition of anonymity, that the fighter jet was targeted on Sunday evening as it was flying in the skies over Kitaf wa al-Boqe'e district in the country's northwestern mountainous province of Sa'ada, Yemen's Arabic-language al-Masirah television network reported.
In November a year ago, the Houthis targeted the Saudi capital, Riyadh, with a ballistic missile that was intercepted by Saudi air defenses.
A spokesman for the Saudi-led military alliance fighting the Huthis in Yemen did not immediately respond to a request for further details.
The conflict is now widely seen as a proxy war between regional rivals Saudi Arabia - which backs the government - and Iran - which backs the Houthi rebels.
The Houthi have previously fired missiles targeting the Saudi mainland, including the capital, Riyadh, the city's global airport and a royal palace - all of which were intercepted by Saudi forces.More news: Fired Google engineer's suit claims reverse discrimination
No casualties have been reported in the attacks.
Since March 2015, Saudi Arabia and some of its Arab allies have been carrying out deadly airstrikes against the Houthi Ansarullah movement in an attempt to restore power to fugitive former President Abd Rabbuh Mansour Hadi, a close ally of Riyadh.
But despite the coalition's superior firepower, the rebels still control the capital and much of the north.
The war still raging in Yemen is the worst humanitarian crisis in the world, according to the United Nations, with at least 10,000 people killed and widespread hunger and disease.