There were no military casualties in the incident near the Palestinian city of Jenin.
A Jenin hospital where the two Palestinians were admitted said a 19-year-old died of his wounds and the other was in stable condition after being shot in the lower back, Reuters reported.
A military statement said troops had opened fire at “two assailants (who) hurled an explosive device”.
Tensions have risen across the Palestinian territories since a move by the United States in late 2017 to recognize the holy city of Jerusalem (al-Quds) in the West Bank as Israel’s “capital.”
The move flew directly in the face of Palestinians’ demand that the city’s eastern part serve as the capital of their future state, and prompted a vote by the United Nations General Assembly soon afterwards that called on Washington to withdraw the recognition.