The officials say a militant drove a piece of construction equipment packed with explosives into Brig Gen Hassan Abbas Toufan's convoy north of the city of Fallujah, while others opened fire.
A colonel and two lieutenant colonels were also killed in the attack, said a member of the division as well as an intelligence officer. There was no information on how many soldiers were also killed.
Both spoke on condition of anonymity because they were not authorized to speak to the press.