Amateur video circulated online of police and civilians on Saturday running through the cafe-lined streets in the seaside metropolis.
Police identified the gunman as Kamel Abu Bakr, 27, from a village near the flashpoint city of Jenin in the occupied West Bank.
The man wounded in the shooting was a municipal patrol worker who was targeted when he approached the suspect after noticing something suspicious. He was taken to hospital “in critical condition” and later died, according to the Magen David Adom emergency service.
“Another municipal inspector responded swiftly and managed to neutralise the terrorist,” police said, adding that “significant police forces are present at the scene”.
“We are standing at a very sad incident,” Tel Aviv’s Mayor Ron Huldai told Israel’s public broadcaster.
The shooter is suspected to be a resident of the Palestinian town of Jenin in the occupied West Bank.
The attack came a day after a settler rampage in the occupied West Bank killed one Palestinian, deepening the spiral of violence that has gripped the region for the past year and a half.
Nineteen-year-old Palestinian Qusai Jamal Maatan was killed when Israeli settlers in the Palestinian village of Burqa in the West Bank. Israeli police said they arrested two Israeli settlers in connection with the violence.
Earlier on Friday, Israeli soldiers shot dead another young Palestinian, 18-year-old Mahmoud Abu Sa’an, during one of their daily pre-dawn raids into the occupied West Bank.
Yair Lapid, an opposition leader in the Israeli parliament, stated violent settler attacks in the West Bank endanger other settlers, describing most as “law-abiding civilians”.
Jenin’s refugee camp last month was the site of the largest Israeli offensive in the occupied West Bank in nearly 20 years. Twelve Palestinians, including at least eight fighters, and one Israeli soldier, were killed in the raid, which forced thousands to flee their homes and left large swaths of the camp in ruins.
Tensions in the occupied territory have intensified since early last year when Israel began its near-nightly raids into Palestinian areas.
More than 200 Palestinians have been killed this year in the occupied Palestinian territories and the Gaza Strip, the majority in the occupied West Bank.
This year is already the deadliest for Palestinians since the United Nations began keeping track of fatalities in 2005.
Israel captured the West Bank in the 1967 Middle East war, along with the Gaza Strip and East Jerusalem. Palestinians seek those territories for their hoped-for independent state.