The bombing was carried out by ISIS in the Jerayshi area in Ramadi on Thursday, controlled by the group.
Two commanders identified as General Abdel Rahman Abu Ragheef and Brig Safeen Abdel Majeed was deployed as deputy commander of operations and divisional commander respectively, reported BBC.
According to media reports, the bomb went off as the army intercepted an explosives-laden vehicle which they believed was targeting them.
The military and the police are battling to recapture Ramadi, supported by Shia militias, Sunni tribal fighters and US-led coalition air strikes.
Ramadi was captured by the ISIS in May one in a series of embarrassing defeats inflicted upon Iraqi forces over the last year - and thousands of civilians fled.