The military helicopter is said to have engaged in "hostile activity" in the area near the border.
Video recordings and photographs of the downed helicopter testify to its fate, according to Sarea.
In his statement, Sarea warned against incursions into Yemeni airspace.
"Yemen was ready to do everything in its power to protect Yemeni airspace from any act of aggression," he said.
The Saudi-led coalition are yet to confirm the reports.
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The downing comes only a day after the release of over 1000 Houthi prisoners by the coalition.
The prisoners, who were captured in different part of Yemen since the outbreak of the war in 2015, were released and flown to the Yemeni capital, Sanaa.
Read more: Freed Houthi prisoners return to Yemen as warring parties hope for peace |
Additionally, backchannel negotiations with the Houthis in Oman remain ongoing, after the rebels claimed an attack on Saudi oil infrastructure that threatened global oil supplies.
The New ArabComments