A police spokesperson said: "The bulldozer driver left a construction site, and hit two cars.
"A civilian who saw what was happening shot him."
Police identified the perpetrator of Tuesday's attack as Ghassan Abu Teir, a Palestinian resident of occupied east Jerusalem.
Al Jazeera's David Chater, reporting from Jerusalem, said that according to police, the assailant had a criminal record.
"This attack was very similar to the one carried out three weeks ago, and has stirred debate as to how the authorities here should respond to such incidents. There have been calls to demolish this man's house, but people are asking whether it is right to punish the family of this 22-year-old man," he said.
While Abu Teir was not known to be part of a wider group, the Hamas movement based in the Gaza Strip labelled the attack as a "natural reaction to the crimes of the [Israeli] occupation".
However, Mahmoud Abbas, the Palestinian president, said he "condemned and rejected" the attack and said such incidents "hurt our reputation and peace in general".