Three of the victims were seriously injured and nine others including the bus driver suffered moderate injuries, a spokesman for the rescue services, Magen David Adom, said.
Pictures released by the police showed a large knife lying on the ground.
The stabbing attack took place on a bus on Menachem Begin road, a major thoroughfare in south Tel Aviv.
The assailant is a 23-year-old man from the West Bank city of Tulkarm, illegally residing in Israel, police said.
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Israel's Internal Security Minister Yitzhak Aharonovich said that the "terrorist was in Israel without work visa".
The stabbing is being treated as a "terror attack," Israel Police foreign press spokesman Micky Rosenfeld said.
Meanwhile, Islamist Hamas, which controls the Gaza Strip and whose charter vows complete destruction of Israel, hailed the stabbing attack on bus commuters as a "heroic act".
The incident is just one of a series of 'lone-wolf' terror 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.