Police spokesman Micky Rosenfeld said the 19-year-old Palestinian stabbed the 42-year-old Israeli in a "terrorist" attack in Yavne.
The suspect was apprehended at the scene, and the victim taken to hospital with "critical" injuries, a later police statement added.
The Shin Bet security agency named the assailant as Ismail Ibrahim Abu Aram, born in 1998, and said he had no previous record of security-related offences.
Israeli soldiers later searched Abu Aram's home in Yatta, near Hebron in the occupied West Bank, a spokeswoman confirmed.
The man manages to fight off the attacker but is stabbed several times.
A wave of unrest that broke out in October 2015 has killed more than 290 Palestinians or Arab Israelis, 44 Israelis, two Americans, two Jordanians, an Eritrean, a Sudanese and a Briton, according to an AFP toll.
Israeli authorities say most of the Palestinians killed were carrying out knife, gun or car-ramming attacks.
Others were shot dead in protests and clashes, while some were killed in Israeli air strikes on the Gaza Strip.
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