"Forces are currently searching for assailant," the tweet said.
The Israeli military added that those killed were father and son.
Friday's shooting marks the latest example of violence in recent weeks in the volatile region.
Israelis have reacted to a spate of attacks -- many of them stabbings, some shootings, and some in which cars were used to hit people -- targeting its citizens in Israel and the West Bank, with Prime Minister Benjamin Netanyahu leading the charge to thwart what he's called a "wave of terror."
Speaking of the latest Hebron attack, Netanyahu said Friday, "We will find the murderers and bring them to justice, like we have done in the past."
Palestinian officials, meanwhile, claim Israeli authorities have repeatedly gone too far. They say that innocent civilians have too often, and unfairly, paid the price.
The Palestinians' official WAFA news agency reports that, since early October, Israeli forces have killed more than 80 Palestinians, a figure that includes protesters who died in clashes as well as alleged attacks. The same report adds that more than 2,240 have been injured.
The Palestinian health ministry said two more Palestinians died Friday -- one of them a 22-year-old from Hebron who was hit in the heart by a bullet fired by Israeli troops clashing with protesters, the other from the same West Bank city who succumbed to his injuries from an earlier clash.
Wherever one stands in this age-old discord, one thing that seems evident to all is that there's no obvious end in sight.
Lately, Hebron has become a focal point in this conflict.
Israeli troops, police and members of the Israeli Security Authority conducted an operation early Thursday in the city's Al-Ahli Hospital to arrest a Palestinian man accused in an October 25 attack in a Jewish settlement in the West Bank, according to the IDF.
During that security action, Israeli authorities killed one of the suspect's relatives, Palestinian Health Minister Jawad Awad said. Throngs of Palestinians took to the streets the next day for the funeral of that man, identified by Awad as 27-year-old Abdallah Shalaldeh.
Palestinians from in and around Hebron, as well as Ramallah, were among those detained late Thursday and into Friday, according to the WAFA news agency
That same agency also reported that Israeli snipers on Friday shot and injured a young Palestinian man near the entrance to the town of Sa'ir.