Falah Abu Maria, 50, was shot in the chest in the village of Beit Omar near the southern city of Hebron, neighbors said.
He had run downstairs at his home to see what was happening when troops stormed it to arrest his son Mohammed, they added.
The hospital said that the 24-year-old son was being treated for a gunshot wound to the leg, AFP reported.
The incident was similar to one on Wednesday near the northern West Bank city of Jenin, where the Zionist regime's troops shot dead Mohammed Alawneh, 22, in clashes that followed raids and searches at several houses in the village of Birqin.
Alawneh was shot in the chest and died shortly after arriving at hospital in Jenin, a Palestinian medical source said.
The shootings came after weeks of low-level violence in the occupied Palestinian territories, and amid regular Israeli arrest operations.
Last month, soldiers shot dead a Palestinian at a checkpoint in the Jordan Valley during the Muslim fasting month of Ramadan.