The command, which oversees Iraq's war effort against the Islamic state group, said casualties occurred on both sides during a strike on IS during close combat.
The incident took place at around 1:00 pm (1000 GMT) south of the jihadist stronghold of Fallujah, military sources said.
Forces from Iraq's 3rd Division 55th Brigade had been advancing on IS positions near Amriyat al-Fallujah but could not be supported by the Iraqi air force due to bad weather, the command said.
"That allowed our forces to achieve quick progress and clash with the enemy in close combat," it said.
"A third coalition strike carried out without taking into account the distance that had been covered resulted in injuries among our forces too.
An officer and nine soldiers were killed or wounded, the command centre said without providing a breakdown.