Israeli border police also stormed a Palestinian university in the occupied West Bank, following more than a month of violence that has raised fears of a third Palestinian intifada, or uprising.
An Israeli in his seventies was left in serious condition after he was stabbed by a Palestinian in Netanya, 30 kilometres north of Tel Aviv.
The attacker was "neutralised", police said.
Earlier, three Israelis were stabbed in attacks near the central bus station in Rishon LeZion, about 10 kilometres south of Tel Aviv, a police statement said.
The foreign ministry said one of the victims was an 80-year-old woman, while the country's medical service said two of the three Israelis stabbed were in severe condition.
The attacker was arrested by security forces after he was locked in the shop, police said.
The attacks were the first outside of the West Bank and Jerusalem since October 22, according to the Israeli authorities.
Nine Israelis, 68 Palestinians -- around half of them alleged attackers -- and an Arab Israeli have been killed in a wave of violence since the start of October.
The violence was originally focused in and around Jerusalem but the epicentre moved to Hebron over the past week.
The random nature of the attacks, and the fact that most of the assailants were apparently acting alone, has made it harder for Israeli security forces to react.
Police also said they uncovered an explosive device when they searched a car today near Hebron.
The last successful bomb attack in Israel was on a bus in Tel Aviv in November 2012, according to Israeli officials.
A second Palestinian, allegedly an accomplice, was arrested.
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