Al-Aqsa Martyrs' Brigades said they planted the bomb which injured a further six people in a restaurant in downtown Tel Aviv on Monday morning.
But despite the Al-Aqsa claim, Israeli police and fire services said the bombing was most likely carried out by a criminal gang.
"It looks more and more like it is a criminal incident because of the circumstances and the kind of explosive that was used," police spokeswoman Eti Greenburg said.
Israeli radio reports said the device was aimed at the head of a debt recovery agency.
They said there was no suggestion the attack was linked to the Israeli-Palestinian conflict.
The unidentified woman died in hospital after the explosion in Yizhak Sadeh street on Monday morning.
Fire fighters said the device blew up in a lift or on its roof, in a building next door to a restaurant.
Initial reports said the blast could have been caused by an exploding gas canister, but fire service chief, Aharon Aharoni, said that explosive material had been found at the scene.
"It was not caused by a gas fault," he said.
Meanwhile, the Israeli military said on Monday that a woman was in serious condition after being shot in the leg by a suspected Palestinian resistance fighter.
The suspected Jewish settler was in a car on a road near a settlement near Nablus in the northern West Bank.
However, her life is not in danger according to medical sources.
After the attack, the army said it combed the area to find the perpetrators.
It added it had arrested a member of resistance group, Hamas and a member of Yasir Arafat's Fatah organisation in separate overnight raids.