The fighter jet was cruising in northern Yemen as part of the Saudi Arabia-led coalition's long-running operations against the Houthi rebels.
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. Riyadh has confirmed the downed jet belonged to the Saudi Royal Air Force.
It made no mention of the Huthis, but said it would continue to "reject and resist aggression and siege" against Yemen, a reference to a military campaign being waged since 2015 by a Saudi-led coalition.
The Houthis shot down the F-15 fighter with a ground-to-air missile, the Houthi-affiliated Saba news agency reported, citing the army's statement. Lowcock said he remained deeply concerned by the deterioration in the humanitarian situation in the country although there has been progress in the past month in opening Yemen's critical Red Sea ports to commercial fuel and food shipments, as well as the resumption of humanitarian shipments and flights.
Kansas election chief charges 2 more with voter fraud
Senate minority leader Chuck Schumer said the commission "never had anything to do with election integrity". But several states expressed concern over how such information might be used by the administration.
Earlier this week, the Saudi state media had alleged that the latest Houthi missile attack into southern Saudi Arabia proved that "the Iranian regime remains implicated in supporting the armed Houthis".
The effectiveness of Saudi Arabia's military intervention is severely questioned as a large swathe of territories are still under the control of Houthi rebels.
United Nations statistics show more than 10,000 people, a lot of them civilians, have been killed since the coalition intervened in the Yemeni civil war that also displaced around three million.