The attack took place along a boardwalk near a beach popular with tourists.
US Vice-President Joe Biden was in a meeting a few kilometres away.
The Magen David Adom ambulance service said four of the injured had severe injuries.
"A terrorist, an illegal resident who came from somewhere in the Palestinian territories, came here to Jaffa and embarked on a run along the boardwalk," Tel Aviv Mayor Ron Huldai told Army Radio.
"On his way he indiscriminately stabbed people."
He said a police officer had eventually caught up with the attacker and shot him dead.
The attack in Jaffa was the third attack by Palestinians on Israelis within just two hours.
An hour earlier, two Israeli Border Police officers were seriously injured in occupied East Jerusalem in a drive-by shooting attack in the main shopping district near Jerusalem's Old City.
In the town of Petah Tikva, local media reported that the Israeli stabbing victim pulled the knife out of his own neck and stabbed his attacker to death.
Mr Biden arrived in Israel late on Tuesday for a two-day visit, and was meeting former Israeli president Shimon Peres in Jaffa around the time of the boardwalk attack.