The incident, near West Bank city of Tulkarm, was the latest in a series of deadly soldier-on-soldier shooting incidents in the Israeli military.
The commander of the elite unit will finish his term and be barred from a command position for the next two years.
Military Police to question officer who shot his commanders on Sunday
Two soldiers were seriously injured during a large-scale West Bank arrest raid in September.
An IDF soldier who accidentally shot and killed his friend was indicted in a military court on Wednesday for recklessly using a weapon, leading to manslaughter.
Defense Minister Avigdor Liberman responded to the decision, saying that he agreed with the dissenting judge and that Amaro must be convicted of murder.
An investigation into death of Staff Sgt. Strug found 3 other similar incidents.
IDF investigating incident in which special unit soldier was shot by fellow soldiers.