Israeli police fired rubber bullets and tear gas inside the Al-Aqsa compound on Sunday after a standoff between Muslim and Jewish worshippers outside one of the gates to the holy site in occupied East Jerusalem.
A Palestinian ambulance service said that at least 14 Palestinians were taken to hospital for treatment.
Al Aqsa mosque, built on top of the Temple mount, is the third holiest site in Islam.
Police lead the arrested man from the scene.
In a bid to ease tensions, police initially barred Jewish visits to the site on Sunday but Muslim worshippers still feared they would be allowed in and protested there.
The day coincided with the Jewish holiday of Tisha B'Av, which typically sees an increase in Jewish visitors to the holy site.
They said the move was in response to police announcing they would consider allowing Jews to ascend the holy site.
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In June, police allowed Jewish visitors onto the site on Jerusalem Day, which fell this year during the final days of Ramadan, sparking clashes between Muslims and police.
Responding to nationalist calls for riots, Muslims on the Temple Mount rioted on Sunday, forcing Israeli police to clear the area using crowd control methods, including stun grenades, Israel media reports.
Sunday marks Tisha B'av, the Jewish memorial day for the destruction of the First and Second Temples, which according to Jewish tradition were destroyed on the same day 585 years apart. Jewish tradition also maintains that Jews should avoid entering the holy site. Israel's Kan public radio said four police officers were injured.
The Palestinian gunman approached the border fence, opened fire at the soldiers who fired back and shot him dead.
While people around the world traditionally head to markets several days before the Eid to buy gifts, candies and new clothes for their families, the impoverished people in Gaza have been marking Eid al-Adha under harsh conditions imposed by the Israeli regime since 2007.
Hamas leader Ismail Haniya spoke of the Al-Aqsa clashes on Sunday, saying it "shows the religious dimension of the conflict".