The Israeli military said four protesters were detained but no one was injured.
Al Jazeera's Nour Odeh, reporting from Ramallah, said the risk of skirmishes is increasing when Palestinians see more Israeli soldiers on the ground, as they do during the 48-hour lock-down.
"What this closure does is raise tensions and so we've seen clashes at the Qalandiya checkpoint as well as in the village of Beit Ummar close to Hebron," she said.
The clashes had been limited and had not resulted in many injuries, our correspondent said.
Israeli imposed the closure amid reports of possible protests by Palestinians around the al-Aqsa mosque in Jerusalem after Friday prayers.
Tension was high in East Jerusalem on Friday.
Some Palestinians threw rocks at Israeli troops. After men under the age of 50 were denied entry to the al-Aqsa mosque, hundreds of men prayed at the gates of the Old City.
Clashes erupted last week after Binyamin Netanyahu, the Israeli prime minister, announced plans to include two sites in the West Bank on a list of Israeli heritage sites.
An announcement from the interior ministry that plans to build 1,600 new Jewish homes in East Jerusalem had been approved also contributed to the tensions.
Israel occupied East Jerusalem after the 1967 war with the Arabs and built settlements that are considered illegal under international law.