Palestinian security sources and medics named the casualty as 50-year-old Ghalia Yunis.
They said she had been shot several times when approaching the Israeli separation wall dividing the settlement of Ganei Tal from the Palestinian community of Qarara.
An Israeli military source said the woman had been hit during exchanges between troops and "militants" who had been firing mortar rounds, anti-tank missiles and rockets at the nearby Gush Katif settlement bloc overnight.
However, he said it was not clear whether she had been hit by the soldiers or fire from the "militants".
"During the night there were several attempts to fire mortar rounds, anti-tank missiles and Qassams (makeshift rockets) at Gush Katif," the source said.
"The IDF (Israel Defence Forces) returned fire with light ammunition at the sources of fire without any identification of any hits of any kind (by the Israelis)."
He added: "We did get reports at a certain point that a woman was hit and we arranged for an ambulance to evacuate her to hospital."