The society quoted the family of 20-year-old Hamza Battah as saying Israeli soldiers shot him in the leg and the abdomen.
Israeli soldiers then detained him and brought him to Shaare Zedek medical center in Jerusalem, in critical condition.
No further details were provided.
An Israeli army spokeswoman did not immediately return calls seeking comment.
On Saturday, two Palestinian youth were injured during clashes with Israeli forces.
Aida camp is a frequent site of clashes because it is located beside Rachel’s Tomb, which is surrounded on three sides by the Israeli separation wall, despite being in the middle of the Palestinian city of Bethlehem.
Israeli forces shot more than 20 youth with rubber-coated steel bullets and live bullets during clashes occurring almost daily in December and January, and clashes continue to break out occasionally in the area.
There are 19 refugee camps in the occupied West Bank, within which live about a quarter of the 771,000 registered refugees in the territory.
More than 760,000 Palestinians — estimated today to number 4.8 million with their descendants — were pushed into exile or driven out of their homes in the conflict surrounding Israel’s creation in 1948.