A Passover animal sacrifice near the mosque compound in the Old City would likely have been perceived by Muslims as a challenge to the tense status quo of the site and could have sparked unrest.
As the Jewish holiday began, Palestinian militants in the Gaza Strip fired a rocket from the Gaza Strip into Israel on Monday, the military said, but there were no reports of any casualties or damage.
In the West Bank, at the checkpoint between Bethlehem and Jerusalem, a small group of Palestinians hurled stones at Israeli security forces, who responded by firing stun grenades.
Jerusalem has been rocked in past weeks by the worst rioting in years, triggered largely by rumours that a rebuilt 17th-century synagogue was part of a plan by Jewish extremists to destroy the revered Al-Aqsa mosque.
An announcement of plans to expand settlement construction in Jerusalem has further fuelled the tension while also angering the US administration and casting doubts over proposed peace talks.
Police said Muslim men under the age of 50 and all non-Muslims were from Monday barred from entering the compound -- which is sacred to both Muslims and Jews. Police did not say when the restrictions would be lifted.
Authorities have also tightened restrictions on access to Israel from the occupied West Bank, closing checkpoints to general traffic.
The restrictions on the Palestinian territory are to be lifted on April 6 after the conclusion of Passover when Jews commemorate their biblical exodus from Egypt. The holiday begins at sunset on Monday.
Israel usually locks down the West Bank during Jewish holidays and has been especially wary in recent months as Palestinians clashed with security forces in and around Al-Aqsa.
Dozens of people were injured in September and again this month when violence broke out following rumours that Jewish extremists intended to pray at the compound.
Security was particularly tight on Monday around the Al-Aqsa compound, the third holiest site in Islam and the holiest for Jews, who call the site Temple Mount.
Muslims are intensely sensitive to any perceived change in the status of the compound and many believe Jews are determined to build a new temple on the wide esplanade, the site of the Second Temple destroyed by Romans in 70 AD.
Jewish fringe groups have vowed to build a third Temple, but Israeli political and religious authorities have repeatedly dismissed the idea.
The status of Jerusalem is one of the thorniest disputes between Israel and the Palestinians.
It has been at the forefront as US efforts to revive moribund peace talks have made little headway amid Israel's refusal to bow to pressure to halt construction of Jewish homes in mainly Arab east Jerusalem.
The US-Israel rupture emerged two weeks ago when Prime Minister Benjamin Netanyahu announced plans to build 1,600 Jewish settlements in east Jerusalem, embarrassing Vice President Joe Biden when he was in the country.
US President Barack Obama during a meeting in Washington with Netanyahu last week asked the Israeli premier to take up a set of confidence-building measures to promote peace talks, according to White House officials.
Benny Begin, a member of the security cabinet, told public radio on Monday that the US demands were proving counter-productive.
"The pressure applied by the Americans will have the opposite effect, inciting Palestinians and Arabs to adopt more extremist positions," said Begin, a minister without portfolio.
"Reunited Jerusalem is the capital of Israel and there is no way we will give up our sovereignty," he added.
Israel annexed east Jerusalem after capturing it in the 1967 Middle East war in a move not recognised by the international community. The Palestinians see east Jerusalem as the capital of their promised state.
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