The attack began in Beit She'an, a town in Israel near the northern border of the West Bank, where a 68-year-old man was hit by the attacker's car, Israeli police said in a statement, according to the AFP news agency.
The Palestinian attacker continued driving and later stabbed an 18-year-old woman to death near the highway. In Afula, a passerby managed to shoot the attacker, who was taken to hospital with minor injuries, The Times of Israel reports.
Two people were also injured in the attack.
Following the attack, the Israeli army has begun planning a raid on the attacker's home village of Qabatiya. Defense Minister Israel Katz has ordered "forceful and immediate" action against the village.
Friday's attack comes just days after Israeli soldiers shot dead a Palestinian teenager in the Qabatiya area. The incident is being investigated internally by the military after images showed that the teenager did not appear to have posed any threat to the soldiers.
On Thursday, an Israeli reservist, dressed in civilian clothes, is also suspected of deliberately running over a Palestinian man in the West Bank.
