The decision will apply until next week, when the Muslim holy month ends, a police spokeswoman told the AFP news agency on Tuesday.
Clashes between Muslims and Israeli police have been taking place every morning since Sunday during protests against Jewish visits to the site during Ramadan.
The Palestinian Red Crescent said on Sunday that its medical team took seven Palestinians to an East Jerusalem hospital for treatment of injuries from sponge-tipped bullets, tear gas and beatings.
Palestinian officials said the trouble began when Israel allowed Jewish visitors into the al-Aqsa compound, the third holiest site in Islam, in breach of a tradition that allows only Muslim worshippers to enter during the last 10 days of Ramadan.
The period, which began on Sunday, is the most solemn for Muslims and it attracts the highest number of worshippers to the site.
Israeli police said officers at the Old City site revered by Muslims and also by Jews – who call it the Temple Mount – arrested four “masked youths who were disrupting visits on the Temple Mount” by non-Muslims.
The al-Aqsa Mosque compound is in the Old City of East Jerusalem, which Israel annexed in 1967 – in a move never recognised by the international community – as part of its occupation of the West Bank.
Jews and other non-Muslims can visit the site but are banned from praying there.