Micky Rosenfeld, an Israeli police spokesman, said two Israeli policemen were also injured in the confrontation.
Also called Day of Atonement, Jews mark Yom Kippur by fasting and holding prayers.
The police entered after Israeli settlers and Zionist groups attempted to force entry to a part of the complex they call Temple Mount.
Other Israeli settler-activist groups also gathered at the Hetta and Majlis gates, Al Jazeera's correspondent said.
Last year, a similar incident on the Yom Kippur holiday resulted in damage to dozens of cars and shops.
Meanwhile, Israeli forces have imposed military closure on Palestinian territories starting from Saturday midnight until Monday midnight in view of the religious holiday.
Israel captured the Old City of Jerusalem during the 1967 Six-Day War and later annexed it along with the rest of mostly Arab East Jerusalem in a move not recognised by the international community.