Two of the victims were seriously injured and several others suffered moderate injuries, a spokesman for the rescue services, Magen David Adom, said.
The stabbing attack took place on a bus on Menachem Begin road, a major thoroughfare in south Tel Aviv.
The attacker tried to flee the scene on foot but was shot and neutralised by the police. He is being questioned.
The assailant is a 23-year-old Arab man from the West Bank city of Tulkarm, illegally residing in Israel, police said.
The incident is just one of a series of lone-wolf attacks in recent weeks as tensions have been rising between Israelis and Palestinians since last June, when three Israeli settlers were kidnapped and killed in the West Bank.
The kidnappings set off a series of events that led to the 50-day Gaza war, which left more than 2,100 Palestinians and 71 Israelis dead.
In November, five Israelis were killed and several more wounded in a terror attack at a synagogue in the Jerusalem neighbourhood of Har Nof, while an Israeli soldier was killed in a knife attack in Tel Aviv, another Israeli woman was stabbed to death in the occupied West Bank in a separate attack.
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