The F-16 jet crashed in the kingdom's southwestern region of Jazan near the border with Yemen, the coalition said in a statement on the official SPA news agency.
The pilot "survived" the crash, it said, without specifying his condition.
The incident comes a day after Bahrain said that three of its soldiers had died "in an incident on the southern borders of Saudi Arabia."
It did not say how they had died or when the incident took place.
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The Bahraini jet is the second coalition F-16 to crash after a Moroccan plane went down during a mission over Yemen in May. Its pilot was later found dead and his body was returned home.
The coalition said that crash had been caused by a technical fault or human error, and it denied rebel claims that they downed the plane.
The alliance has been backing forces loyal to Yemeni President Abedrabbo Mansour Hadi's internationally recognised government with air strikes, ground troops, and weaponry, in addition to training.
Sudan has also deployed troops in Yemen while Kuwaiti media reported this week that the emirate has decided to send ground forces.