He was hit in the flashpoint district of Issawiya where police faced off with stone throwers during a demonstration by residents protesting the closure of most access roads to the area.
Clashes erupted in the early morning after around 100 people, including schoolchildren, tried to block the main road leading from east Jerusalem to the Dead Sea.
Police fired tear gas, percussion bombs and sponge rounds as masked youths hurled stones at them, police and an AFP correspondent said.
Sponge rounds are made from high-density plastic with a foam-rubber head, and are fired from grenade launchers.
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Police have been using them in Israel and occupied east Jerusalem since the use of rubber-coated metal bullets was prohibited, but protocol explicitly prohibits firing them at the upper body.
The boy was rushed to the nearby Makassed hospital then transferred to Hadassah Ein Kerem in west Jerusalem, where a spokeswoman said he was conscious and in moderate condition.
Paramedics treated another 16 residents for tear gas inhalation after a police gas canister hit a local bus, they said.
Home to some 20,000 Palestinians, Issawiya lies in the valley east of the Hebrew University on Mount Scopus, close to the main road to the Dead Sea.
Local activist Raed Abu Riyaal told AFP the parents' committee had decided to protest over police action to cut off three of the district's four entrances with concrete blocks.
He said a group of young residents had decided to block the main road "in order to put pressure on police to reopen the main entrances."
The court has given the state until Wednesday to file its response.