Two of the victims were seriously injured and several others suffered moderate injuries, Magen David Adom said. Others at the scene were treated for shock.
The injured were evacuated to the Sheba Medical Center at Tel Hashomer and Ichilov Hospital at Sourasky Medical Center in Tel Aviv.
The attacker fled on foot but was shot and neutralized by police and is being questioned. The assailant is a 23-year-old man from the West Bank city of Tulkarm, illegally residing in Israel, police said.
Tel Aviv police chief Bentzi Sau said the attacker, reportedly a resident of the Tulkarem West Bank who had entered Israel illegally, boarded the bus about 400 meters away from where the incident began. He first attacked the driver, then began stabbing a number of bus passengers.
Police beefed up security in the city to help locate possible accomplices, and have asked the public to increase awareness.