The compound, known to Muslims as the Al-Aqsa mosque but to Jews as the Temple Mount, is holy to both religions.
Visits by Israeli officials during Jewish holidays are considered provocations by many Palestinians, who fear Israel wants to take control of the third holiest site in Islam.
The Temple Mount is the holiest site in Judaism.
"The ban on ministers and MPs was decided for security reasons" during the eight-day Passover festival, police spokesman Micky Rosenfeld said, without giving further details.
"However, the visits of tourists and Jewish visitors can continue normally," he said.
Under the current arrangement, Jews are allowed to visit the compound but not pray.
Rosenfeld added that police reinforcements had boosted their presence in Jerusalem during the festival, with a total of 3,500 police on patrol. He declined to say how many of these forces were new.
"These forces are patrolling in all public places, bus stations, shopping malls, tram stations," he said.
During Passover tens of thousands of Jews flock to the Old City of Jerusalem.
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Last year 50,000 Jewish worshippers attended a ceremony held in front of the Wailing Wall, which will be held on Sunday this year.
The site is venerated by Jews as a remnant of a wall supporting the Second Temple complex, which was destroyed by the Romans in 70 AD.
The wall is located below the mosque compound in the Old City in Israeli-annexed East Jerusalem.
Israel has also closed off all crossing points between the occupied West Bank and the Gaza Strip to Israeli territory for Friday and Saturday.
Prime Minister Benjamin Netanyahu announced last week Israel would deploy reinforcements around the Temple Mount during Passover to prevent "riots".
"As Passover approaches, all sorts of extremists will spread lies about our policy concerning the Temple Mount," he said.
Tensions are high in Israel following a wave of violence that has killed 201 Palestinians and 28 Israelis since October.
Most of the Palestinians killed were carrying out knife, gun or car-ramming attacks, according to Israeli authorities.
Palestinians argue that Israel is seeking to change the arrangement at the Temple Mount, claims Netanyahu and other ministers have repeatedly denied.
Passover celebrates the escape of the Israelites from slavery in Egypt.