Hospital officials said three Palestinians suffered bullet wounds in the clashes in Jenin, a militant stronghold and the scene of deadly fighting during a Palestinian uprising a decade ago. There were no reported Israeli casualties.
The military said about 300 Palestinians, including some who "hurled explosives and opened fire", confronted soldiers who entered Jenin looking for the three seminary students.
Israel says the Hamas Islamist group abducted them last week as they were hitchhiking near a Jewish settlement.
It said 30 "terror suspects" were detained in the West Bank, bringing to 280 the number of Palestinians taken into custody over the past week.
Israel has said its West Bank operation is two-fold: to find Gil-Ad Shaer and US-Israeli national Naftali Fraenkel, both aged 16, and Eyal Yifrah, 19; and to deal a substantial blow to Hamas, a group dedicated to its destruction.
Palestinian president Mahmoud Abbas accused Israel of using the teenagers' disappearance as "a pretext to impose tough punishment against our people and besiege them" in violation of international humanitarian law.