"Technical reasons" caused the crash of the US-built aircraft in the Najran district on the Saudi side of the border with Yemen, the coalition said.
It added that the pilot was in good condition.
The rebels´ Al-Masirah television website claimed that the fighter-bomber had been shot down by "anti-aircraft defences".
Separately, the United Arab Emirates army command announced the death of one of its soldiers fighting in Yemen as part of the coalition.
He was the second Emirati soldier in a week to die in Yemen, raising to around 80 the number of troops from the UAE killed in coalition operations against the Huthis and their allies.
The coalition launched air strikes, training and other military assistance nearly two years ago to support Yemen´s President Abedrabbo Mansour Hadi.
The rebels are allied with former members of the security forces loyal to ex-president Ali Abdullah Saleh.
In March last year, two Emirati pilots were killed when their Mirage warplane crashed in Yemen because of what the coalition called a "technical fault".
Three months earlier, a Bahraini pilot survived when his F-16 crashed in Saudi Arabia , reportedly also for technical reasons.
A Moroccan air force pilot died in May 2015 when his F-16 went down in Yemen, with the coalition blaming human error or a technical fault.
Two Saudi F-15 pilots were rescued when they ejected from their jet off Yemen´s coast shortly after coalition air strikes began.
Rights groups have repeatedly criticised the coalition bombing campaign over high civilian casualties.