The driver of the vehicle was killed when a police officer and a taxi driver shot him, police said.
"A police officer at the site saw the tractor lifting the police vehicle into the air and opened fire at the driver," Niso Shaham, deputy head of Jerusalem police, said.
"Several seconds later a taxi driver joined in" the firing, he said.
Police said the identity of the driver was not immediately known.
"The driver apparently belonged to the Arab minority ... We could not immediately identify the driver because he did not have an identity card on him," Shaham said.
Jacky Rowland, Al Jazeera's correspondent, said: "It is always possible that it could have been an accident but there have been a number of tractor attacks in the last year in Jerusalem, where Palestinians have used diggers as weapons against pedestrians and motorists."
Hamas, the Palestinian movement which has de facto control of the Gaza Strip, said it supported the apparent attack.
"The operation in Jerusalem was a natural response to aggression against our people. The Zionist enemy should realise that they alone bear the responsibility for displacing our people in Jerusalem and for the killings in Gaza and the West Bank," Mushir al-Masri, a senior Hamas official, said.
A Palestinian was shot dead in July after he killed three Israelis and wounded 45 others by ramming a bulldozer into buses and cars in central Jerusalem.
Three weeks later 16 people were hurt in a similar incident, in which the attacker was also killed.