It was not immediately clear who planted the device on a road in the capital Sanaa, then detonated it as Fawaz al-Dhibri's vehicle went past, the sources added. All four were in a stable condition in hospital.
Yemen has been plunged into turmoil since pro-democracy protests in 2011 forced president Ali Abdullah Saleh to step down after 33 years in office. Authorities have since struggled to rein in rival political factions and tribes, southern separatists and Islamist insurgents.
Dhibri is the director of the office of General Ali Mohsen al-Ahmar, who broke away from the army during the anti-Saleh protests and said he was siding with the demonstrators.