Media reports say order is part of preparations to evict Jewish settlers.
About 40 people were hurt in clashes between police, settlers and Palestinians during the eviction operation on Thursday.
About 30 Jewish settlers were injured, mostly due to smoke inhalation, while three policemen were injured by settlers, who threw rocks, food and chemicals at them.
The settlers, some armed, set fire to Palestinian cars and property near the building.
Eight Palestinians were hurt, including three of them from bullet wounds.
Al Jazeera’s correspondent spoke to one of the victims, Hosni Swaifan.
“Once settler came into our house. He took a gun and shot me and he shot my dad, and then thousands came down in front of the army. Then there were clashes between the army, police and settlers. They started burning the houses, it lasted four hours” he said.
One of the shootings was filmed by a volunteer for a rights group.
Thirteen families were reportedly living in the house, which is in a key strategic location between the settlement of Kiryat Arba and the Cave of the Patriarchs, a holy site for Jews and Muslims.
Settler violence flared in other areas of the Israeli-occupied West Bank with security forces moving to quell the protests, although Palestinian residents said settlers had blocked roads and thrown stones at their cars causing damage.
By around midnight on Thursday, Hebron residents reported clashes had largely died down and an army spokesman said there were no reports of major incidents across the West Bank.
Four Hebron settlers were later arrested while more than 20 of their supporters in Jerusalem were taken into custody after briefly blocking a main entrance to the city, police said.
The settlers say they lawfully purchased the building from Palestinians.
But Faiz Rajabi, a Palestinian Hebron resident, said that the building belongs to him and denied having sold it to the settlers.
“Thank God, the building has returned to its owners and I hope they will not come back,” Rajabi said.
Mahmoud Abbas, the Palestinian president, has called on Israel to evict all 650 settlers who live in fortified enclaves in the heart of Hebron, home to some 180,000 Palestinians, an aide said.