Police said fighting began when Arab residents of the Silwan neighbourhood stoned a security guard in his vehicle.
"A guard responsible for protecting Jewish residents of the neighbourhood opened fire with his pistol after his car was attacked with stones," spokesman Micky Rosenfeld said.
Witnesses said another two Palestinians were wounded in the shooting. Several others were injured later as police fired rubber bullets and tear gas at stone-throwing protesters in and around the neighbourhood.
Police said the security man had found himself trapped by a makeshift barricade set up by Palestinians.
"The guard found himself in a situation where his life was endangered after he came upon a pre-planned ambush," Israeli public radio quoted Jerusalem police chief Aharon Franco as saying."He was obliged to fire."
"They simply ambushed him," Channel Two TV quoted him as saying.
Franco told Channel One TV in an interview that after initial questioning the man was freed without charge, on his own bond, pending further enquiries.
"At the end of the day he was released," Franco said. "We shall continue the investigation at the beginning of next week."
The dead man, Samir Serhan, had been detained in the past for "participation in unrest," Rosenfeld said.
Palestinian residents and local officials said they did not see what sparked the violence.
"We were awakened by the sound of gunfire at 4:00 am (0200 GMT) and when we came down we found Samir's body on the front steps," a cousin of the deceased said, adding that the dead man left behind five children.
There was fresh trouble during his funeral, with Palestinian youths hurling stones at police cars and other vehicles, setting three cars on fire, including a police cruiser, and shattering the windows of a public bus.
Army radio reported that 10 Israelis were wounded in the violence, including three police, and that eight Palestinians had been arrested.
Police spokesman Shmuel Ben-Ruby said that after dark, molotov cocktails were hurled at police in Silwan but nobody was injured.
Earlier, police briefly entered the Al-Aqsa mosque compound in pursuit of a stone-throwing youth but did not enter the mosque itself.
Silwan, where a few dozen Jewish families live in a guarded enclave surrounded by 12,000 Arab residents, is one of the most volatile areas of east Jerusalem, which Israel occupied in 1967 and later unilaterally annexed.
The neighbourhood adjoins the walls of the Old City and the mosque compound, which is the holiest site for Jews because it was the location of the Second Jewish Temple, torched by the Romans in 70 AD.
The compound is the third holiest site for Muslims, after Mecca and Medina.
It has frequently seen violence and was the epicentre of the outbreak of a Palestinian intifada, or uprising, almost exactly 10 years ago.
Wednesday's clashes highlighted the challenges negotiators face in peace talks which resumed on September 2 after a 20-month hiatus.
"This violent escalation by the Israeli occupying forces represents destructive measures that defeat the peace-building agenda," said Ghassan Khatib, a spokesman for the Western-backed Palestinian Authority.
The international community considers Israeli settlements in the West Bank, including east Jerusalem, to be illegal.
The Palestinians want a freeze on all settlement construction but are also pushing for the renewal of a partial moratorium on new West Bank settler homes that will end within days, even though it does not include east Jerusalem.
Israel does not define Jewish residents of east Jerusalem as settlers as it views the entire Holy City as its "eternal and indivisible capital."