Palestinian medics said at least 14 people were wounded, one seriously, in the skirmishes with police at the site, which Muslims refer to as the Al-Aqsa mosque compound and Jews refer to as the Temple Mount.
Preacher of the Al-Aqsa Mosque compound Ikrima Sabri told Xinhua in a telephone interview that the Israeli police "stormed into the Al-Aqsa Mosque compound and tried to evict worshippers out of it by force".
Police lead the arrested man from the scene.
This Sunday, Muslims across the globe are celebrating Eid al-Adha, also known as the "Festival of Sacrifice", an Islamic holiday marking the end of the annual hajj pilgrimage to the city of Mecca in Saudi Arabia.
The Muslim celebrations coincided with the Jewish holiday of Tisha B'av, which sees an increase in Jewish visits to the Al-Aqsa compound.
Some 1,300 Jews visited the site on Sunday, according to the Muslim Waqf organisation, which administers the holy compound.
In a move never recognised by the worldwide community, Israel annexed the entire city in 1980, claiming it as the self-proclaimed Jewish state's "eternal and undivided" capital.
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.
But some settler groups have been lobbying Israeli authorities to allow Jewish visitors on the site during Tisha Be' Av, so they can mourn the destruction of a temple believed to have been located there 2,000 years ago.
The police cited the presence of tens of thousands of Palestinian worshippers and the high possibility of clashes. Jewish tradition also maintains that Jews should avoid entering the holy site.
The separate incident on the Gaza border followed two similar ones since the start of the month.
The clashes came amid heightened tensions between Israel and the Palestinians, just days after an Israeli soldier was killed south of Jerusalem.
Hamas leader Ismail Haniya spoke of the Al-Aqsa clashes on Sunday, saying it "shows the religious dimension of the conflict".