The incident occurred last Wednesday in an industrial zone in Giubiasco, near Bellinzona, when a 60-year-old motorist from Bellinzona was reversing on the road.
He did not see the boy who was struck and suffered serious injuries.
It is not clear what the child was doing on the road or who was supervising the infant.
The toddler was transported to a local hospital for treatment before being transferred to a special clinic in Basel for treatment, the Corriere del Ticino newspaper reported.
The newspaper said the boy died in the Basel treatment centre on Monday morning.
It has been a tragic week for two-year-olds in Switzerland.
The infant’s death in Basel follows reports of two children aged two, who went in missing in separate incidents over the past two weekends in the cantons of Saint Gallen and Aargau.
Searches for the children have so far been unsuccessful.