The Palestinian health minister warned that the situation was "critical" in Jenin, with many other people injured and ambulances unable to reach them.
The children's ward of a local hospital was hit by Israeli tear gas, she said.
Israel's military released few details, but Israeli media said it had acted to foil "a major attack" by militants.
The Palestinian militant groups Hamas and Islamic Jihad said they were battling Israeli troops in the flashpoint town, where there have been repeated Israeli raids.
Tensions have recently risen in the West Bank as the Israeli military continues what it describes as an anti-terrorism offensive.
At least 29 Palestinians have been killed by Israeli forces in the West Bank so far this year, including militants and civilians.
Last year, more than 150 Palestinians were killed, nearly all by Israeli forces, while a series of Palestinian attacks targeting Israelis, as well as militant gunfire at troops during arrest raids, killed more than 30 people, including civilians, police and soldiers.