The deaths on Monday came a day after Israeli forces raided two Gaza refugee camps, killing 14 Palestinians including three boys, a civilian adult and 10 gunmen.
Palestinian security sources said Khaled Madi, 16, was helping his father in the family fields in southern Gaza during a school holiday when Israeli soldiers opened fire on them killing the boy. Medics said Madi was shot in the head.
Israeli military sources confirmed that soldiers on patrol near the Morag settlement in southern Gaza fired "warning shots" and said they were checking if anyone had been hit.
Later on Monday, Israeli undercover soldiers shot dead a 30-year-old Palestinian grocer in the West Bank town of Salfit while trying to arrest a man suspected of being a member of an armed group linked to Palestinian President Yasir Arafat's Fatah movement.
Medics said the grocer, also named Khaled Madi, was one of three people wounded in the incident, including the suspected group member, and that he died of a critical gunshot wound to the abdomen while on the way to hospital.
An Israeli military source said soldiers opened fire when the wanted man tried to flee arrest, wounding him and then taking him into custody. Reports of other casualties were being checked, the source said.
Violence has escalated in the Gaza Strip since Israeli Prime Minister Ariel Sharon announced a unilateral plan last month to evacuate Jewish settlers from the coastal region if a US-backed peace "road map" fails.