Army spokesman Jonathan Conricus said the 23-year-old Palestinian had worked in the Barkan industrial zone, where the attack took place in the occupied West Bank.
Conricus called it a "terrorist attack" but added that other unspecified factors were involved.
The Palestinian used a homemade gun in the attack, known locally as a Carlo, according to Conricus.
He said it appeared it was a "lone-wolf attack".
Security forces were searching for the suspected perpetrator, Conricus said.
Magen David Adom emergency medical services said their medics had entered a building at Barkan where they found a man and woman without pulse, and pronounced them dead.
A woman aged 54 was also found wounded and in moderate condition, the medical services said.
Speaking at the beginning of the weekly cabinet meeting, Prime Minister Benjamin Netanyahu called the shooting "a very severe terror attack".
He said he was certain the perpetrator would be caught and brought to justice.
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.
The industrial zone is located next to Israeli settlement Barkan and near the settlement of Ariel in the north of the West Bank.
Palestinians work side by side with Israelis in the industrial zone.
A wave of Palestinian attacks against Israelis broke out in 2015, but they have since become sporadic.
Last month, a Palestinian teenager stabbed an Israeli to death at a junction at the entrance to a large bloc of Israeli settlements in the West Bank near Jerusalem.
A number of attacks have occurred at that location, the Gush Etzion Junction.
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