Police are calling the incident a terrorist attack, although officials said they believed Husam Taysir Dwayat, 30, acted alone, The Jerusalem Post reported.
Sixty-six others people were injured, officials said. The bulldozer flattened about six cars, and overturned and severely damaged several other vehicles, including a bus.
Dwayat -- a Palestinian living in east Jerusalem -- drove down a busy thoroughfare in west Jerusalem, ramming into vehicles before heading toward a market, police spokesman Micky Rosenfeld told CNN.
"We believe he acted on his own and tried to kill as many people as possible," Rosenfeld said.
The rampage lasted 4-5 minutes before an off-duty police officer shot Dwayat, who cried "Allah Akhbar" (God is great) before he died, the Post said.
Police said three terrorist groups claimed responsibility for the attack, including the al-Aksa Martyrs Brigade, affiliated with the Fatah movement in Palestine; the Galilee Freedom Battalion, suspected of being affiliated with Hezbollah; and the Popular Front for the Liberation of Palestine, a fringe terror group.