The Saudi Black Hawk "fell during operations in the province of Marib" east of Sana'a, the coalition said in a statement carried by the Saudi Press Agency, without clarifying the reason.
At least 12 Saudi military personnel were killed Tuesday - including four officers - when their helicopter crashed in eastern Yemen, Saudi-led coalition commanders have said.
Also on Tuesday, the USA defence secretary James Mattis began a week-long tour of the Middle East and eastern Africa in Saudi Arabia, for talks on regional security, with Yemen and Syria leading the agenda.
The Saudi-led coalition accuses Iran of trying to use the Houthis to expand its influence in Yemen, one of the poorest Arab countries.
The Saudis have also lost dozens of soldiers in cross-border attacks from Yemen.
In 2015, a ballistic missile fired by the Houthis towards a coalition military base in Marib killed more than 60 troops from the United Arab Emirates, Saudi Arabia and Bahrain. To that end, Mr Mattis has asked for the lifting of restrictions imposed by that former president Barack Obama on arms sales to the kingdom.
The Houthi-run Saba news agency said the helicopter crashed in an area known as al-Tadaween, northeast of the Marib provincial capital, and that 13 officers and soldiers had died.
Multiple rounds of U.N-brokered peace talks have failed to bridge the gap between the warring parties in Yemen.