The video, widely circulated on social media, shows the uniformed officer curse the driver, then headbutt him in the face and kick him in the legs.
Other Palestinians are seen trying to reason with the policeman only for him to turn on them also.
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Thursday's police statement said the officer was notified of the decision on Wednesday and his dismissal would take effect within 14 days.
"It was an exceptional and violent incident which goes against all the values of the Israel Police," it said.
"A policeman who behaves in such a manner has no place in the Israel Police."
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A Palestinian witness filmed the incident, which took place in a car park near the interior ministry in the Wadi Joz area of annexed east Jerusalem, and handed a copy to an Israeli journalist.
The witness said the policeman had accused the driver of having damaged his car with the truck.
Shortly after the incident the police condemned the attack and suspended the officer.
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