The Israeli human rights group, B'Tselem, says settlers shot and wounded three Palestinians.
According to Israeli Haaretz newspaper, stones were hurled by settlers at Palestinian cars in Nablus, Ramallah and Hebron.
The Jerusalem Post reports that settler youths set fire to a number of Palestinian homes and cars.
There are fears the attacks could plunge the West Bank into further communal violence.
Maj-Gen Amos Gilad, the Israeli military co-ordinator in the Palestinian Territories, has met Palestinian Authority Prime Minister Salam Fayyad to urge him to restrain Fatah forces throughout the West Bank.
But the governor of the Nablus region, Jamal Moheisin, has warned that if Israel did not control the settlers, "we will call on the Palestinian residents to go out to the streets and fight back".
Ownership of the building is in dispute.
The settlers say that they bought the house from its Palestinian owner for nearly $1m (£660,000), but the owner says he pulled out of the deal.
It took several soldiers to remove each settler from the house
The Israeli Supreme Court authorised that the building to be cleared of its occupiers until another court could decide who owned it.
Israeli Defence Minsiter Ehud Barak said the building would be handed over to the guardianship of the Israeli military until the dispute was resolved. Settlers denounced the military action.
"This could have been done peacefully and legally. Instead Barak chose violence," said Danny Dayan, leader of the Yesha settler council. "This surprised us completely. He threw a match in a pile of gun powder."
But legislator Avshalom Vilan, a member of the left-wing Meretz-Yahad party, defended the evictions as a victory for justice.
"This was a test for the rule of law and it shows there is one law for everybody for people in Hebron, Tel Aviv and everywhere," he said.
It was the most significant fight between hard-line settlers and the Jewish state in three years, says the BBC's Tim Franks near the scene.
The house is in a strategically important position between Hebron's Jewish settlements and an important religious site sacred to both Jews and Muslims.
About 600 Jewish settlers live in the city, with several thousand more in surrounding settlements.
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