They say the blast in Marib province today also injured 15 people. The officials spoke on condition of anonymity because they were not authorized to speak to the media.
Maj-Gen Abdul-Rab al-Shadadi was killed last week while leading an offensive against Shiite Houthi rebels east of Sanaa. He was the most senior officer to be killed in Yemen's civil war this year.
His brother, Salem al-Shadadi, was killed in Friday's blast. Troops and militiamen loyal to President Abed Rabbo Mansour Hadi's government have been fighting the Houthis and their allies since 2014. A Saudi-led coalition intervened on Hadi's side last year.