Najeh Btirat, an official with the Muslim clerical authority that administers the compound, said the clash followed a mosque sermon on the issue.
"The Friday sermon focused on the Islamic sites that are being targeted by Israel and the need to preserve them," he said. About 300 young men threw stones at police after prayers, he said.
Sherine Tadros, Al Jazeera's correspondent in Jerusalem, reported: "Medical sources are telling us that a lot of the Palestinians who were injured were fired on by rubber bullets from the Israeli police.
"But that is something the Israeli police tell us did not happen - they have not been using any ammunition live or otherwise."
Mickey Rosenfeld, the Israeli police spokesman, told Al Jazeera that police used only the "minimum ammount of force" against the protesters.
"Only stun grenades were used, in fact, to disperse those rioters. Nine of our officers were injured at the scene and treated in hospital," he said.
"Our main aim is to continue a calmness - a respectable calmness - on the Friday prayers on the Temple Mount, as well as in East Jerusalem."
The compound, which is known to Jews as the Temple Mount and to Muslims as the Noble Sanctuary, has been the site of a number of such incidents.
Clashes there on Sunday have been linked in part to a decision by Binyamin Netanyahu, the Israeli prime minister, to include two sites in the occupied West Bank on a list of Israeli heritage sites.
Skirmishes also broke out after Friday prayers in the West Bank city of Hebron, but no serious injuries were reported.
A group of about 100 Palestinians protested outside the holy site known to Jews as the Cave of the Patriarchs and to Muslims as the Ibrahimi mosque.