The shooting broke out in the densely populated Palestinian refugee camp of Balata, in the Israeli-occupied city of Nablus, when police went to arrest suspects, Wafa said, quoting officials.
Police spokesman Adnan al-Damiri identified the policeman who died as Hassan Ali al-Hajj and said he was shot dead by Ahmed Abu Hamada, also known as "Zaabur".
Abu Hamada, who was wounded in the gunfight, was wanted by for murder, the possession of weapons and trafficking, as well as opening fire on police, said Damiri.
The governor of Nablus told Wafa that a second policeman was slightly wounded in the shootout.
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The suspect was eventually arrested, said Wafa.
Balata - the largest Palestinian refugee camp in the West Bank home to 30,000 people - saw an uptick of violence last year when Palestinian security forces launched raids to seize illegal weapons.
There are frequent clashes between police and armed men who are holed up in the camp.
One of the men, Hatem Abu Rizeq, 30, recently told AFP he does not "trust Palestinian security forces" and those like him tracked by the authorities are constantly in fear of being "executed".