The tractor "crashed into an Egged bus that hit another private vehicle. A policeman who saw what happened fired ... killing the terrorist," police spokeswoman Luba Samri said.
The bus was empty of passengers, and only the driver suffered mild injuries.
A 30-year-old pedestrian who was hit by the tractor was critically injured and eventually succumbed to his wounds after efforts to resuscitate him failed.
Six others were injured in the accident, Magen David Adom rescue services personnel said.
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The slain terrorist's family was being questioned, he said.
The minister also cautioned the public that further attempts to carry out terror attacks were possible, emphasising that security forces were prepared to handle such incidents.
This is the third such attack in Jerusalem when an industrial digger has been used to attack people on the streets in the last six years.
Palpable tension could be felt in the city since an Arab boy was kidnapped and killed in a revenge attack after three Jewish teenagers were kidnapped and later found murdered.