The compound - known as "Haram al-Sharif "and "Temple Mount"- is a holy site for both Jews and Muslims.
There were clashes in on the streets of Jerusalem after Israel shut announced it was closing the compound to visitors for the first time in 14 years.
The closure came amid fears of violence. Tensions have flared after US born Jewish activist Yehuda Glick was shot on Wednesday. He survived the attack and is recovering in hospital.
Glick had had been campaigning for Jewish access to the sacred site.
Israeli police then killed a Palestinian man accused of shooting him, 32-year-old Muataz Hijazi.
Access to the al-Asqa mosque is a sensitive issue. Israel routinely restricts entry for young men, citing fears of violence.
Many Jewish Israelis have also been arguing their case for the right to pray there.
Palestinian president Mahmud Abbas condemned the closure of the compound as a "declaration of war".
"This dangerous Israeli escalation is a declaration of war on the Palestinian people and its sacred places and on the Arab and Islamic nation," Abbas said through his spokesman Nabil Abu Rudeina, warning it would only fuel "more tension and instability".
But a spokesman for Israeli Prime Minister Benjamin Netanyahu said the closure aimed "to prevent riots and escalation as well as to restore calm and status quo to the Holy Places".
Police spokeswoman, Luba Samri, said the shrine would open early on Friday for dawn prayers, after midnight.
Samri said that because of fear of unrest, entry for Muslim men would be restricted to those over 50.
There would be no such restrictions on Muslim women.
In another development Palestinians say is linked to the closure, Sweden has become the first major Western European country to officially recognise Palestine as a state.
Palestinian President Mahmoud Abbas hailed the decision as “brave and historic”.
While, Israeli Foreign Minister Avigdor Lieberman denounced the move as "deplorable", in a bizarre Facebook post in which he said relations in the Middle East were “more complex than assembling IKEA furniture”.
Israel has recalled its ambassador from Sweden for "consultations".
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