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.
He said the two crew members were rescued unharmed and returned to Saudi Arabia.
Maliki gave no further details.
A coalition statement released later by the official Saudi Press Agency said the warplane that crashed was Saudi and that the operation to rescue the crew involved ground forces.
Huthi rebels, who are locked in a war with Yemen’s government, said they shot down the plane over Saada, their northern Yemeni stronghold, according to their Al-Masirah television channel.
The Saudi-led coalition joined the Yemeni government in its fight against the Huthis in March 2015, after the rebels seized control of the capital Sanaa.
Despite the coalition’s superior firepower, the rebels still control the capital and much of north Yemen.
More than 8,750 people have been killed since the coalition intervened in Yemen, according to the World Health Organization.