The wounded man was evacuated to the Hadassah University Hospital in Ein Karem.
Later video footage showed Israeli forces conducting raids in the nearby village of Kafl Hares, in the northern West Bank.
Palestinian security sources named him as Hamza Zamareh, 17, from Halhul, near the scene of the attack. The Palestinian Red Crescent ambulance service said stone-throwers had clashed with the soldiers.
The identity of the dead man did not match that of the suspect given by Israeli authorities as the stabber.
A Fatah spokesman, Osama Qawassmeh, said that death of Jarrar, who was killed in a shootout with the IDF, was "a type of field execution" and an Israeli "crime" that violated global law.
Israeli forces have been widely condemned by rights groups for what have been deemed "extrajudicial killings", in situations where alleged assailants could have been detained in a non-lethal manner.
Israel's Shin Bet domestic security agency said that "during the attempted arrest, the terrorist came out of a building where he was hiding armed". It said a "Qassam bullet" was responsible for the murder, though it was unclear if the Hamas leadership was claiming direct responsibility for the attack or whether the cell acted on its own.
Tensions have risen since US President Donald Trump's controversial recognition of Jerusalem as Israel's capital.
The U.S. move drew condemnation from across the region and sparked angry protests in the Palestinian territories - and multiple clashes with Israeli troops - that have so far left at least 24 Palestinians dead. Two Israelis have been killed in that timeframe.