Palestinians hurled stones at Israeli police who responded with tear gas during the clashes.
Prime Minister Benjamin Netanyahu urged the authorities to swiftly investigate the "reprehensible murder" and called on all sides "not to take the law into their own hands".
Tensions have mounted between Israel and the Palestinians after the bodies of three Israeli teens were found in the West Bank more than two weeks after they went missing. Israel has accused Hamas of abducting and killing the three teenagers and has arrested hundreds of its members.
Meanwhile, rocket fire from the Hamas-controlled Gaza Strip has intensified and has been met with Israeli air strikes.
Israeli police spokesman Micky Rosenfeld said police received a report an Arab teenager was "forcibly pulled into a vehicle" in an area of east Jerusalem and that an hour later a body was discovered.
He said security was heightened in Jerusalem, with extra units dispatched and the city's light rail train service cut short to avoid the scene of the violence.
Police also closed a key holy site in Jerusalem's Old City to visitors after rock throwing there.
Israeli officials urged calm as police investigated the incidents, hoping to contain the violence.
Public security minister Yitzhak Aharonovitch said: "Everything is being examined. There are many possibilities. There is a criminal possibility as well as a political one. I am telling everyone, let us wait patiently."
Nabil Abu Rdeneh, a spokesman for Palestinian President Mahmoud Abbas, said Israel was being held responsible for the death and called on it to "find the killers and hold them accountable".
The Arab teenager, who was identified as 17-year-old Mohammed Abu Khdeir, was approached by a car and then forced into it before it sped off, his cousin Saed Abu Khdeir said.
On Tuesday, thousands attended the funerals of Eyal Yifrah, 19, Gilad Shaar, 16, and Naftali Fraenkel, 16, the three Jewish seminary students who went missing last month and whose bodies were found on Monday in a field near the West Bank city of Hebron.
While the teenagers were laid to rest in the city of Modi'in, several hundred Israeli demonstrators, some chanting "death to Arabs", blocked the main entrance to Jerusalem.
Cries for revenge have echoed throughout the decades-old Israeli-Palestinian conflict.
They can be heard at the emotionally charged funerals of Palestinians killed by Israel and the phrase "May God avenge his death" is often invoked at the burials of Israelis slain by Palestinians.
But deadly Israeli vigilante attacks, in declared retribution for Palestinian assaults, have been rare in recent years.
More common are incidents in which mosques and Palestinian property is torched or damaged.
Tensions are also high in the West Bank, where around 40 Palestinians were arrested in raids on Tuesday, the latest in a campaign by Israel to cripple Hamas there. Four people were shot and wounded during an Israeli raid in the Palestinian city of Jenin yesterday.