An Israeli military source said the soldier was lightly wounded by fragments of glass from a window which was shattered by a gunshot as he drove near the isolated settlement of Morag on Monday.
Sources within the Palestinian security services, which are patrolling the outskirts of the evacuated 21 Gaza settlements, said it was believed the shots came from the nearby Palestinian town of Khan Yunus.
No Palestinian group has claimed responsibility for the attack, which comes a day after a bomber blew himself up and critically wounded two security guards at the central bus station in Beersheba.
Palestinian groups have largely respected calls by Palestinian president Mahmoud Abbas to hold their fire during the pullout operation which saw the last of the Gaza settlers evacuated last Monday.
Also on Monday, two Palestinians were killed and a third was wounded in an explosion in a refugee camp.
Witnesses said a man, accompanied by two sons, was collecting scrap metal in the Askar refugee camp.
Palestinian security officials said the man was cutting through an old Israeli military shell found in a pile of debris when it blew up on Monday.
The explosion killed the man and one of his sons, while the other youth was wounded, they said.
The Israeli army said it was not involved in the blast, but said it was looking into the report that an old shell had exploded.
Meanwhile, EU foreign policy chief Javier Solana was meeting Israeli and Palestinian leaders on Monday as the international community tried to breathe life back into the peace process after the Israeli settler pullout from Gaza.
Solana’s tour coincides with the arrival of the head of the Egyptian intelligence services, Omar Suleiman, who is expected to urge resistance groups to continue adhering to a truce agreement brokered in Cairo.
The top European diplomat on Monday continued a round of meetings with Israeli officials, including Defence Minister Shaul
Mofaz and Deputy Prime Minister Shimon Peres.
He was later to meet Palestinian President Mahmoud Abbas in Gaza City and Prime Minister Ahmad Qureia on Tuesday.
The European Union, along with the United States, United Nations and Russia, is one of the sponsors of the road map which targets the creation of an independent Palestinian state alongside a secure Israel.