The friendly fire incident follows an escalation in fighting between the Houthis and Yemeni government forces around the central city of Marib.
An air strike by the Saudi-led coalition has mistakenly hit a camp of allied Yemeni pro-government forces, killing at least 12 troops.
The strike, which took place on Thursday in the province of Shabwa, also wounded at least eight Yemeni troops, officials said on Friday.
Officials spoke on condition of anonymity because they were not authorised to brief the media.
There was no immediate comment from the Saudi-led coalition. Turki al Maliki, a coalition spokesman, did not respond to numerous media calls and messages.
At the scene of the strike, several bodies were burned and three military vehicles, some of which carried automatic rifles, were destroyed, according to two local residents.
Friendly fire incidents where Saudi-led coalition air strikes have hit allied ground forces have happened on occasion during Yemen's conflict.
Yemen has been torn by civil war since 2014, when Iran-backed Houthi rebels overran the capital of Sanaa and much of the country’s north.
In 2015, the Saudi-led coalition intervened to halt the rebels and restore the internationally recognised government to power.
However, the war has slogged on for years and created the world’s worst humanitarian crisis.
In the past months, fighting has escalated between the Houthis and Yemeni government forces around the central city of Marib and the coastal city of Hudaida.
The coalition has also increased its air strikes on Sanaa and other rebel-held areas in Yemen in recent weeks.