It was the third deadly arrest operation in less than a week.
Border police forces entered the Qalandia refugee camp near Ramallah to arrest two "suspected terror activists," police said.
One of them was shot in the leg as he was running away across a roof, then fell to his death as he tried to leap to another roof, they added.
Palestinians identified the dead man as Mohammad Abu Latifa, 18.
Police said the forces had called on Abu Latifa to stop, before shooting at his lower extremities.
"Despite that, the suspect continued to run and when he attempted to get to the roof of another building, he fell off it and was mortally wounded," a statement said.
A paramedic with the troops attempted to treat Abu Latifa, but was forced to pronounce him dead at the scene, police said.
The two suspects were suspected of having "planned a terror attack in Israel," according to the statement.
On Wednesday, troops shot dead a Palestinian during clashes near the northern West Bank city Jenin.
Israeli authorities say the arrest raids are necessary to detain suspects and that troops can face dangerous rioting during the operations.
Palestinians, however, condemn the raids in the occupied territories, and the Hamas and Islamic Jihad militant groups hinted at revenge after Thursday's death.
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