Medical sources said 45-year-old Fada Aram and her son Abd Allah were killed when the tank shell exploded late on Sunday night.
The blast also wounded Fada's 54-year-old husband Sulaiman.
An Israeli military source confirmed that tanks in the sector had opened fire on two occasions - once on "suspects who were digging a hole with the apparent intention of planting a bomb" and once on "suspects who were observing our troops".
"It is not our intention to fire on civilians and we are investigating this incident," the source added.
But since the beginning of the al-Aqsa Intifada, over 3500 Palestinians have been killed, including more than 650 children. Some 28,400 have also been seriously injured.
Over 1000 Israeli have been killed in the same period, including 117 children and almost 7000 injured.