The television report blamed three members of the opposition for shooting down the plane. The incident came as anti-government protests continue to attract huge crowds.
The plane crashed near Arhab north of Sanaa, the report said.
A fighter in Arhab said the plane was used to attack people in the area.
"The government is attacking and killing our loved ones because they have the weapons. We have to fight back and we will do so," Abdullah al-Shaleef said.