The soldier and the policeman were lightly wounded while the attacker was moderately wounded, the army said.
Security camera footage from the incident published by Israeli media showed a silver vehicle appearing to accelerate and collide with a parked police car.
Palestinians have carried out dozens of stabbing, shooting and car-ramming attacks on Israeli security personnel and civilians in recent years. Most were by lone Palestinian attackers with no apparent links to armed groups.
Palestinians and human rights groups have frequently accused Israeli security forces of using excessive force.
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