The shooting occurred just before 6:30pm at the Shackleford Crossings shopping centre near the city's western edge. The collection of stores has a Walmart on one end and a J.C. Penney on the other. On the last weekend before Christmas, it was crammed with shoppers.
Among them were the grandmother and the little boy, whose identities have not been released.
The woman's car was stopped at a stop sign near the J.C. Penney, police said.
Police say the grandmother didn't know the man in the car behind her.
Without warning, he opened fire, police said, striking the 3-year-old. The boy died at a children's hospital a little later.
Buckner called the crime "senseless".
"The community should do things that you shouldn't have to ask the community to do, which is to be law-abiding," he said. "We cannot have a community to where the least protected among us - being infants - are dying in these senseless crimes."
Little Rock police launched a manhunt for the assailant, but they released only a vague description of the suspect - a tall black man in an older black Chevrolet Impala.
Saturday's shooting comes less than a month after another fatal shooting of a small child riding in a car in Arkansas's capital.
Two days before Thanksgiving, a 2-year-old was fatally shot in the back seat of her mother's car on South Harrison Street, six kilometres east of the scene of Saturday's shooting, according to the Arkansas Democrat-Gazette.
Both shootings remain unsolved.