The fatal shooting happened January 3, at Mac's Speed Shop on McPherson Church Road. The victims were identified as brothers Timothy and Daniel Nakamoto.
After reviewing surveillance footage and other evidence, investigators determined the soldier acted in self-defense, according to Fayetteville police.
Fayetteville Assistant Police Chief Todd Joyce said the argument began over a misunderstanding involving apparel and quickly escalated into a physical confrontation.
"I would say that the conflict arose over someone's misinterpretation of maybe some apparel," Assistant Police Chief Joyce said. "But it went from that to an assault to two individuals, unfortunately, losing their lives."
Police said the shooter, who has not been publicly identified, did not know the brothers and sustained a concussion during the incident. Authorities said the soldier called 911 while leaving the restaurant.
Because the shooter is an active-duty service member, the Army Criminal Investigation Division has taken over the case. No charges have been announced.