According to Al-Ikhbariya TV-channel, the crash took place in the Marib province during a combat mission. The casualties include four officers and eight non-commissioned officers.
Saudi Press Agency said the cause of the crash has not yet been established.
Some reports suggest that the aircraft was shot down accidentally.
Yemen has been suffering from a brutal conflict between the government and the Houthi movement backed by army units loyal to former President Ali Abdullah Saleh since 2014. In March 2015, the Saudi-led coalition of mostly Persian Gulf countries started carrying out airstrikes against the Houthis at the request of governmental forces.