The crackdown comes amid a flare-up in nine months of deadly violence as the end of the Muslim fasting month of Ramadan looms, and after the major diplomatic players called for urgent steps by both sides to revive the moribund peace process.
Troops closed all exit roads from Hebron except for the main northern one through the town of Halhul towards Jerusalem, an AFP correspondent reported.
The army announced on Friday that it would close off the flashpoint city and deploy two additional battalions to the area.
The measures were described as the "most substantial steps on the ground" since 2014, when Israeli forces carried out a huge search operation in the southern West Bank for three young hitchhikers abducted and later found murdered by Palestinian militants.
Hebron has been one of the main focuses of the wave of deadly unrest that has rocked Israel and the Palestinian territories since last October.
At least 214 Palestinians, 34 Israelis, two Americans, an Eritrean and a Sudanese have been killed.
The army has said that around 80 of the attacks on Israelis have been carried out by Palestinians from the Hebron area.
Several hundred Jewish settlers live in a tightly guarded enclave in the heart of the city of more than 200,000 Palestinians, a persistent source of tensions.
On Thursday, 19-year-old Palestinian Mohammed Nasser Tarayra broke into the Jewish settlement of Kiryat Arba on the outskirts of Hebron and killed 13-year-old Israeli-American Hallel Yaffa Ariel in her bedroom before being shot dead by a security guard.
And on Friday, 48-year-old Michael Mark was killed after his car was fired on by a suspected Palestinian gunman south of Hebron.
The army was conducting searches for the gunman on Saturday but there were no immediate reports of any arrests.
An army spokesman said the closure was "intended to break the chain of lethal attacks."
"The physical presence will also disrupt, prevent and foil additional attacks, inspired by the attackers of the last 48 hours," Lieutenant Colonel Peter Lerner told AFP.
'They must feel the consequences'
On Friday, Sarah Tarayra, 27, was shot dead after drawing a knife on Israeli forces in Hebron. She was a relative of the Kiryat Arba attacker, and both were from Bani Naim, a village just outside Hebron.
Lerner said the army had revoked the Israeli work permits of all residents of the village.
The army said no decision had been taken on how long the closure would remain in place, but Internal Security Minister Gilad Erdan said it should stay "for an extended period of time."
"The terror and incitement atmosphere in the Hebron area is backed by the public and local leadership, and they must feel the consequences of their murderous acts in their daily lives," he said in a statement.
In a report released on Friday, the Middle East diplomatic Quartet of the European Union, Russia, the United Nations and the United States said Israel's persistent expansion of Jewish settlements in the Palestinian territories was "steadily eroding the viability of the two-state solution".
It called on Israel to halt its demolition of Palestinian homes and confiscation of Palestinian land.
But it also urged the Palestinian Authority to act "to cease incitement to violence and strengthen ongoing efforts to combat terrorism, including by clearly condemning all acts of terrorism".
The Quartet's recommendations are to serve as the basis for push to revive the Middle East peace process which has been comatose since US-brokered talks collapsed in April 2014.
The group said the Palestinian Authority's lack of control over the Gaza Strip, which is run by the Islamists of Hamas, was another major obstacle, along with the "dire humanitarian situation" in the territory which has been devastated by three wars since 2008.
A rocket launched from Gaza hit the southern Israeli city of Sderot on Friday, causing damage to a building but no casualties.
There was no immediate claim for the fire but Israel responded with air strikes early on Saturday against four facilities run by Hamas and the smaller Islamic Jihad militant group.
They were empty at the time and there were no reports of casualties.