Two Israelis were critically injured and later died of their wounds in the attack that took place in an industrial area near the settlement of Barkan in the central West Bank, according to the Israeli Broadcasting Corporation.
It said security forces "arrested" an unspecified number of people "suspected of aiding the terrorist" while a manhunt for the gunman was still underway.
Among those detained were Na'alwa's brother and sister, the Shin Bet confirmed.
A source from the Palestinian Authority's security services told the Ynet news outlet that its forces were assisting in the search for Na'alwa.
Advocates of Israeli settlement policies say the industrial zones are an example of the benefits Palestinians have under Israeli control, including much-needed employment to Palestinians.
On Sunday morning, Na'alwa arrived to the offices of the Alon Group factory in the Barkan industrial zone armed with an illegally manufactured Carlo-style submachine gun.
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Naalwa was employed at the same plant in the northern West Bank site as his two victims - Kim Levengrond Yehezkel, 28, and Ziv Hagbi, 34.
The other woman shot in the incident was taken to hospital, where doctors said her injuries were not life-threatening.
A wave of Palestinian attacks against Israelis broke out in 2015, but they have since become sporadic. As of now we know nothing about the circumstances. "That's what I think happened".
The Palestinian Islamic Jihad militant group called the attack a "natural response" to Israeli crimes in Gaza, Jerusalem and Khan al-Ahmar, a Bedouin village in the West Bank slated for demolition.
Barkan industrial park is next to the settlement of Barkan and was established in the early 1980s.
Speaking at Israel's weekly cabinet meeting, Prime Minister Benjamin Netanyahu called the shooting "a very severe terror attack".