Security camera footage showed the suspect taking a weapon out of his backpack and shooting.
Israeli security forces have launched a massive manhunt for the gunman, cordoning off areas of the city.
The incident took place in Dizengoff Street, a busy part of the city centre filled with bars and cafes.
It was not immediately clear what motivated the shooting, which follows a wave of Palestinian attacks against Israelis over the past few months.
Police spokesman Micky Rosenfeld told the BBC: "It's not clear what the background of the incident is, if it's a terrorist attack or if it's criminal-related."
Four of the wounded had suffered serious injuries, he said.
Undercover units and counter-terrorism units were working in different areas of Tel Aviv, Mr Rosenfeld said, adding that no specific warning of an attack had been received.
Israeli media are reporting that the attacker has been identified as an Israeli Arab from northern Israel.
The Times of Israel reported, citing police sources, that his father had recognised his son in security footage and called police.
While 1 January is not New Year's Day in the Jewish state, Friday afternoon would be the peak of the weekend and this was a party area of Tel Aviv.
The city tends to be slightly more remote from the political tensions and violence affecting other parts of Israel and the occupied Palestinian territories.
There has been speculation that if the bar was popular with the gay community, it may have been a hate crime. It remains a possibility that there was some kind of link to organised crime.
But until the perpetrator is captured, it is not clear what the motive may have been.
A spokesman for the Israeli ambulance service, Zaki Heller, said people inside and outside the bar had been hit:
"Some of the wounded were inside the pub. Three of them were lying unconscious and the rest were on the sidewalk [pavement]," he said.
Footage from a neighbouring food store shows the gunman - who appears to be a young man, wearing protective glasses or sunglasses, and dressed in dark clothes - choosing dried fruits or nuts.
Moments later, he returns the items, gets an assault rifle out of his bag, leaves the shop and can be seen opening fire from near the doorway.
He is believed to have made off on foot.
Afterwards, broken glass could be seen on the pavement outside the bar and a nearby cafe which was also targeted.
Osnat David, who owns a nearby hair ,said she and her customers had hidden while the shooting took place.
"We were shaking," she said. "There were about eight of us, hiding in the storage room."
The shooting took place at around 15:00 local time (13:00 GMT) on Friday.
As of 23 December, at least 21 Israelis had been killed in the recent violence, most of them in stabbings and shooting attacks by Palestinians.
At least 131 Palestinians have also been killed. More than half were said by Israel to be attackers. Others have been killed in clashes with Israeli forces.
Two people have died and and seven others have been injured after a gunman opened fire with an automatic rifle at a bar in Tel Aviv, Israeli police say.