The 17-year-old was shot in the leg east of Beit Lahiya, after the soldiers had fired warning shots in the air, said the medics, adding he was being treated at the town’s Kamal Adwan hospital.
The Israeli military had no immediate comment on the reported shooting.
On Monday, Israeli fire killed a 21-year-old Palestinian farmer near Beit Lahiya, the fourth such dead in Gaza since a November 21 truce between the Jewish state and the Islamist group Hamas ended eight days of hostilities.
As part of the truce agreement, Israel has allowed Palestinians to enter what was previously a 300-metre (yard) deep no-go zone on the Gaza side of the border.
Farmers have been allowed to move up to 100 metres from the border, but Israeli troops have opened fire multiple times at Palestinians they say have come closer than that.
The youth wounded on Friday was not a farmer, according to the Palestinian sources.