Sam Fahd Abu Haikal, wrapped in a white shroud and a Palestinian flag, was buried in Hebron after funeral prayers were held at a nearby mosque.
The infant was killed on Friday while travelling with his family by car near the city of Hebron.
"What happened to us is not a matter of an apology. What happened is not that shots were fired by mistake and led to this tragedy," the child's father, Fahd, said on Saturday.
"To say it happened by mistake, that 'I didn't know you were coming here,' or that the bullet passed through by accident - no. There is no such thing as 'by mistake' in this case."
The Israeli military has said a single shot was fired after soldiers "perceived a vehicle accelerating toward them".
It has acknowledged that "uninvolved civilians" were injured and said that the incident was under review.
According to the child's grandmother, Firyal, the family had stopped their car after seeing Israeli soldiers in the Tel Rumeida area, south of Hebron.
Shots were fired, the grandmother said, with one bullet piercing the car, killing Abu Haikal and wounding his parents.
"Immediately after the presence of the occupation forces, a soldier holding his weapon opened fire on us. The bullets struck the car," Fahd said.
"The soldier that shot at us was 10 metres away. The bullet penetrated the front windshield, went through my arm and then struck my son in the head and my wife in the face."
The military has not identified the soldiers involved nor said if those soldiers were still carrying out their duties while the review into the shooting was underway.
