According to Qaim Mayor Ahmed Mahallawi, a parked vehicle exploded inside a car wash where members of the Shia-dominated Hashd al-Shaabi militia, also known as the Popular Mobilization Forces (PMF), were stationed.
The explosion killed one PMF member and wounded two others. The blast also killed an employee at the car wash.
It was not immediately clear who was responsible for the attack.
However, Anbar was once under the control of the self-proclaimed Islamic State during its height in mid-2014 to 2017.
Iraqi forces and PMF troops liberated the area, which lies on the border of neighboring Syria, in December 2017.
Despite declaring a military defeat against the terror group shortly after, Iraq is still plagued with sporadic attacks in areas liberated from the Islamic State like Mosul and even places it never controlled like Baghdad.
Indeed, senior leaders in the Kurdistan Region have continually warned that the terrorist organization may re-merge if the root causes which led to its emergence in the first place are not addressed accordingly.