Muslim women will not be affected, although "visitors from other religions will be barred from entering", Micky Rosenfeld, an Israeli police spokesman, said.
Police reinforcements deployed around east Jerusalem amid the tensions in the city will remain in place, he said.
'Adding to tension'
Sherine Tadros, Al Jazeera's correspondent in Jerusalem, said that while Israel was characterising the closures as "standard procedure", the timing itself was "irregular".
"It's an irregular move - over a time that's not a Jewish holiday. We haven't seen that happen here for several years ... [and] that has not been met silently by Palestinians, who are not happy about these continued restrictions on their freedom of movement," she said.
"One of the reasons perhaps why these closures are continuing, especially in the Old City, is that over the next three days a series of events and commemorations are taking place by the Jewish community to celebrate the opening of the Hurva synagogue."
The Hurva synagogue, which was destroyed in the 1948 Arab-Israeli war and rebuilt after Israel seized control of the site when it expanded its borders in 1967, will be officially re-opened on Monday.
Nour Odeh, Al Jazeera's correspondent in the West Bank, said the extension of the closure will only add to the frustration there and lead to more clashes.
"This closure brings the tension to the surface. There are more soldiers so there is more friction," she said.
West Bank clash
On Saturday Israeli troops clashed in the West Bank with Palestinian women and youths protesting against the settlement plans.
Two Israelis were slightly injured on Saturday night when a petrol bomb was hurled at cars on a highway linking Jerusalem and Tel Aviv, police said.
Restrictions have been enforced since March 5 when police battled Muslim protesters at the mosque after weekly prayers.
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.