The Moroccan Royal Armed Forces earlier said one of its planes was missing.
If confirmed, it would be the first coalition aircraft to be shot down since air strikes began on 26 March.
The bombardment has been stepped up in recent days ahead of the start of a proposed five-day humanitarian ceasefire.
Saudi Arabia says its offer of a pause in hostilities from 23:00 (20:00 GMT) on Tuesday to allow aid deliveries is conditional on the Houthis reciprocating.
The rebels have agreed to the truce, but say they will "respond" to any violations.
The 10-nation coalition launched air strikes against the Houthis and allied army units loyal to Yemen's ousted former president Ali Abdullah Saleh with the aim of restoring the government of exiled President Abdrabbuh Mansour Hadi.
Morocco backed the intervention from the start and put at the coalition's disposal a squadron of F-16s already stationed in the UAE for the campaign against Islamic State militants in Iraq and Syria.
On Monday, a Moroccan Royal Armed Forces statement said one of the F-16s had gone missing while flying over Yemen at around 18:00 (15:00 GMT) on Sunday. A second F-16 on the same mission was not able to see whether the pilot ejected, it added.
Later, al-Masirah reported that "air defence of the tribes shot down a warplane over Wadi Nushur", a valley in the Houthis' northern heartland of Saada province.
The channel broadcast footage of tribesmen celebrating around what appeared to be the wreckage of a plane, and holding a piece bearing the roundel of the Royal Moroccan Air Force.
Overnight, the Houthis' northern heartland of Saada was bombed for the third consecutive day, after the coalition declared the whole province a military target, the AFP news agency said.
Rebels in the third city of Taiz and the eastern province of Marib were also reportedly attacked.
Along Saudi Arabia's border with the provinces of Saada and Hajjah, Houthi fighters traded heavy artillery and rocket fire with Saudi troops, residents told the Reuters news agency.
There were no immediate reports of casualties. The UN says more than 1,400 people, most of them civilians, have been killed since 19 March.
Analysts say the coalition appears to be trying to inflict as much damage as possible on the Houthis and their allies before the humanitarian ceasefire starts.
On Sunday, a group of 17 international aid agencies warned that five days was not sufficient to restock food, medicine and fuel supplies in a country under blockade.