They were shot in their car near the settlement of Otniel, in the deadliest such attack for over a month.
It comes amid a surge in attacks, mainly stabbings, on Israelis since the beginning of October.
Elsewhere, two Palestinians were shot dead in clashes with Israeli troops, and another died after being wounded in clashes on Thursday, Palestinians said.
The Israeli military say the gunman opened fire on the car carrying the father, son and other members of the family.
Israeli media identified the victims as Yaacov Litman, 40, and 18-year-old Natanel. Another son, aged 16, was wounded.
A security operation is under way around the Palestinian village of Yatta, near Otniel, as Israeli forces search for the attacker.
Israeli Prime Minister Benjamin Netanyahu condemned the killing, vowing to "find the heinous murderers and... bring them to justice".
Meanwhile, two Palestinians were shot dead in clashes with Israeli troops on Friday, Palestinian health officials said.
Yusuf Awad, 22, was killed near Ramallah, the Palestinian health ministry said, while 23-year-old Hassan Jihad al-Baw was shot dead in Halhul, north of Hebron, Palestinian medics said.
Earlier, Palestinian Mahmud Shalaldeh, 18, who was shot by troops in clashes in Hebron on Thursday, died from his injuries.
The clashes erupted following the funeral of Mr Shalaldeh's relative, shot dead during an undercover Israeli raid on a hospital in Hebron to seize a suspect in the stabbing of an Israeli.
Twelve Israelis and dozens of Palestinians have been killed in recent unrest.
Many of the Palestinian fatalities were attackers in near-daily stabbings of Israelis, shot by their victims or security forces.
The surge in violence began in September when tensions at a flashpoint holy site in Jerusalem revered by Jews and Muslims boiled over, amid rumours that Israel planned to relax long-standing rules to strengthen Jewish rights at the complex.
Israel has repeatedly denied such claims.
A Palestinian gunman has killed an Israeli father and son in the southern West Bank, Israeli officials say.