The boy was hit in the northern West Bank town of Jenin on Thursday, medical sources said.
Gun battles reverberated through Jenin after more than 30 Israeli occupation army Jeeps moved into the city and two Apache helicopters circled overhead.
The operation was targeting members of the Islamic Jihad, which carried out a bombing in Israel on 26 October, after troops arrested 17 suspects in the West Bank overnight, Palestinian sources said. The 26 October blast was carried out in response to Israel's assassination of a leading Islamic Jihad figure.
Call for calm
Under intense pressure from Israel and Washington to disarm armed resistance groups, Abbas delivered his appeal on the first day of the Muslim holiday of Eid al-Fitr.
"The situation should be calm and all these clashes that have erupted here and there should stop," Abbas said after prayers in Gaza City.
Palestinian President Abbas
called for an end to the clashes
In the worst flare-up since Israel's historic pullout from the Gaza Strip in September, 15 Palestinians and six Israelis have been killed in Middle East violence since a 26 October bombing.
The Gaza withdrawal had sparked hopes from the international community for a genuine breakthrough in the peace process, but continued violence saw Hamas vow on Wednesday not to renew an informal truce at the year-end.
Despite calls from the Palestinians for the United States to intervene to end Israeli military operations, Washington has defended Israel's right to self-defence and instead urged the Palestinians to act against armed groups.