Palestinian security officials said on Saturday the army identified the bomber as Abd Allah Badran, 21, a university student, and informed his family.
The army said troops had carried out a raid on the village of Dir al-Ghusun, north of the town of Tulkarim, and that a curfew had been imposed but gave no further details.
Aljazeera's correspondent Muain Shadid said dozens of Israeli military vehicles took part in Saturday morning's raid and that checkpoints were set up around the village.
Among those arrested were two of Badran's brothers and the local imam, Palestinian officials said. One of Badran's brothers works for the Palestinian police, Shadid reported.
The nightclub attack, just before midnight on Friday, killed four Israelis and wounded dozens more.
Israel earlier this month said it would no longer destroy the homes of bombers - a practice once common - because a review by the army concluded it did not deter attackers but inflamed hatred.