Police spokeswoman Luba Samri said the stabbing incident took place as officers were redirecting traffic around a fallen tree on a highway in the Palestinian village of Al-Auja, in the Jordan Valley of the West Bank.
The teen stabbed the officer in the shoulder, and he ran after her and arrested her without firing any shots, Samri said.
Earlier, gunshots were fired at a police car near a Jewish settlement in the West Bank, lightly wounding another officer. Troops searched the area for the shooter.
Also today, the armed wing of Islamic Hamas movement said one of its militants died accidentally while working in an attack tunnel in Khan Younis in the southern Gaza Strip.
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The Qassam Brigades identified the dead as Mohammed Astal, 31. It gave no further details. Fourteen Hamas militants have died in tunnel collapses so far in 2016.
In the 2014 Israeli war with Hamas, attack tunnels from the Gaza Strip into Israel proved to be a greater threat than rockets fired from the coastal enclave.
In Israel, 66 soldiers and seven civilians were killed. The border area has since remained largely quiet, but Hamas has boasted it has rebuilt its tunnel network.