Al-Quds Mufti, Sheikh Ahmad Hussein was arrested because he decried the mosque's closure.
In a separate incident on Friday, Israeli forces shot dead an 18-year-old Palestinian during a raid in Dheisheh refugee camp south of Bethlehem in the occupied West Bank.
"When [the suspects] saw policemen they shot toward them and then escaped toward one of the mosques in the Temple Mount compound".
All three had documents identifying them as Israeli citizens. He said the authorities had issued an order preventing the three men from being named by the media.
Friday's shooting from inside the walled compound in Jerusalem's Old City killed two Israeli policemen.
Jordan, the custodian of the compound, also urged Israel to "immediately reopen" the mosque and denounced the violation of rules at Al-Aqsa.
The Temple Mount/Haram al-Sharif is the holiest site in Judaism and third holiest in Islam and is one of the most politically sensitive sacred places in the world.
"We have urged our Palestinian people to rush to Al Aqsa today and every day to hold their prayers".
Mohammed Hussein, based at the shrine, was taken to an Old City police station, his son Omar said.
Police are reporting that it was "apparently a shooting attack".
The spokesperson warned of the impact of this incident on the peace process, as well as reviving efforts and negotiations between Palestinians and Israelis. No group claimed responsibility, though the Palestinian Islamist group Hamas, which rules the Gaza Strip, praised the attack.
This latest round of violence - sometimes referred to as the "Stabbing Intifada" - began in 2015 and although the attacks have become less frequent they have not stopped.
In the past two years, Palestinian assailants have killed 45 Israelis, two Americans and a British tourist in various attacks involving stabbings, shootings and auto crashes.
"Israel and the Jerusalem police, in particular, are complicit in violating the ban on non-Muslim worship on the holy esplanade", he added.
An Israeli police spokesperson said that the decision to close the mosque was a response to the "dangerous, extreme, and exceptional" attack this week, and that it is to "maintain public safety and order".
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