According to Israeli sources, a Palestinian attacked a police officer with a knife during a security check in Israel.
He then shot him, police said on Tuesday.
The attacker was a man from Hebron in the south of the West Bank.
The police officer was slightly injured in the incident in the coastal city of Ashkelon.
After four attacks in Israel with a total of 14 dead, the Israeli army has expanded its anti-terrorist operation in the occupied West Bank.
Several Palestinians have been killed in military operations, but also in their own attacks.
Israel fears more acts of violence during the Muslim fasting month of Ramadan, which began earlier this month.
On Thursday, a Palestinian from the West Bank shot dead three people in the Israeli coastal city of Tel Aviv.