The Palestinian health ministry said two men were killed in the fighting. Official news agency Wafa identified them as Abdullah al-Hosari, 22, and Shadi Khaled Najm, 18.
Troops arrested Imad Jamal Abu al-Heija, a freed prisoner, Wafa reported.
The news agency said the killing of the two Palestinians sparked a "massive and angry march" in Jenin.
The arrest raid is one of several recent high-profile Israeli incursions into West Bank cities.
Last month, Israeli troops killed three Palestinian suspects during a daylight raid in the northern West Bank city of Nablus.
Israel captured the West Bank from Jordan in the Six-Day War of 1967. It has since built a string of settlements across the territory that is considered illegal under international law but are home to some 475,000 Israelis.