Ibrahim al-Nablusi was responsible for a series of attacks on Israeli soldiers in the area, dpa news agency quoted the Israeli domestic intelligence service Shin Bet and the military as saying in a joint statement.
During the attempted arrest, explosive devices and other weapons were found.
The Palestinian Ministry of Health confirmed the death of al-Nablusi and two other people.
About 40 people were injured by gunshots during the operation.
It is feared that the killing of al-Nablusi could lead to further confrontations.
After three days of fighting, a ceasefire between Israel and the Palestinian Islamic Jihad organization in the Gaza Strip came into effect on Sunday.
The Israeli military had launched the military operation dubbed “Breaking Dawn” with airstrikes targeting Islamic Jihad in the Gaza Strip on August 5.
Two jihadi military chiefs were killed during the operation.
Since the beginning of the fighting, Palestinian militants have fired more than 1,000 rockets at Israeli settlements, according to military sources. Two hundred of them hit the Gaza Strip.
The operation against Islamic Jihad in the Gaza Strip is to be seen as a continuation of a campaign in the West Bank that has been going on for months.
Since a wave of terror in Israel in the spring, the army has been carrying out more anti-terrorist operations there.