In a statement carried by the Saudi Press Agency, the coalition said it was investigating the cause of the crash, which took place in Saudi Arabia's border province of Jizan.
Yemen's Saba news agency, run by the Houthi movement, said Houthi forces had shot down a Saudi Apache helicopter in Jizan.
The coalition named the two pilots as Ali Bin Mohammed Al Qarni and Nasser bin Mohammed Al Harthy.