The policeman was directing traffic after a tree fell and blocked a road in the town of Auja, in the Jordan Valley north of Jericho, when he was stabbed in the shoulder, police said.
The girl ran off but was caught and arrested by her victim.
Israeli police gave her age as 14. Palestinian security sources said she was 16.
A wave of violence in Israel and the Palestinian territories since October has killed 180 Palestinians as well as 28 Israelis, an American, a Sudanese and an Eritrean, according to an AFP toll.
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Others were shot dead by Israeli forces during clashes or demonstrations.
Many of the attackers have been young Palestinians, including teenagers.
Israeli forces have been accused of using excessive force in some cases, which they strongly deny. No shots were fired in today's incident.