Maya Gouzare, a 21-year-old Danish volunteer with the peace-advocacy group International Solidarity Movement (ISM), was wounded after being hit in the back by a rubber-coated bullet, medics and peace activists said on Sunday.
An ISM spokesman said Gouzare underwent an operation at Hebron's al-Ahli hospital, but was expected to face a second surgery later in the day due to complications caused by the bullet.
In another incident, 14 Palestinians sustained injuries from rubber-coated bullets fired by Israeli security forces trying to break up a demonstration in Bait Awwa village, some 15km west of Hebron, medics said.
Six of them were taken to hospital, medics said, adding that about 30 protesters were also treated for tear-gas inhalation.
Palestinian sources said several demonstrators were throwing stones at Israeli forces during the scuffles.
Work on the southern section of the vast separation barrier was stepped up in September after a double bus bombing in the southern Israeli city of Beir Saba.
The bombing was carried out by Palestinian fighters from Hebron.