Aramin was killed when she was hit by a rubber bullet while walking home from school after buying sweets in the West Bank with her sister and two friends.
In Monday's civil ruling, Judge Orit Efal-Gabai dismissed the possibility that Aramin had been struck by an errant stone, determining gunfire as the cause of death.
"It is clear that Abir's death, caused by a rubber bullet shot by border guards, was due to negligence by the defendant"
Orit Efal-Gabai, Israeli judge
"There is no debate over the conclusion that Abir was injured by a rubber bullet shot by border guards, which in turn leads to the conclusion that the shooting of Abir occurred out of negligence, or in violation of the rules of engagement," the Israeli newspaper Haaretz quoted the judge as saying.
"We are not talking about injury by shots fired at a crowd of rioters and rock-throwers, near which a little girl just happened to be standing."
In her ruling, Efal-Gabai said the girls were walking down a street where there were no rock-throwers and therefore, no reason to shoot in their direction.
"It is clear that Abir's death, caused by a rubber bullet shot by border guards, was due to negligence by the defendant."
Israeli police investigated the incident but decided against indicting the border guards who opened fire.
Aramin's family and a human rights organisation Yesh Din challenged the government's decision in the high court but the judges ruled there was no basis for a criminal trial.