Ghulam Mohammad Wagay (70), who was carrying Azra Jan, was hit by a load carrier at Kanidajan near Chrar-e-Sharief, a police spokesman said.
He said the baby died on the spot while Wagay received serious injuries and was shifted to hospital.
In another accident, 8-year-old Tauseef Ahmad Mir of Warnoo-Lolab was hit by a cab at Kralpora near Chadoora and died on the spot, the spokesman said.
The erring drivers have been arrested and separate cases registered against them, he said.