Israeli police earlier said the late Sunday blast in Israel's commercial hub was a "terror attack" that prompted heightened alert.
The force had reported that one person -- who Israeli media said was the suspected assailant -- was killed, and another wounded.
The armed wings of Hamas and Islamic Jihad, which have both fought against Israeli forces in the Gaza Strip, said in joint a statement that they "carried out the suicide operation that took place Sunday evening in the city of Tel Aviv".
The groups threatened to carry out more such attacks in Israel "as long as the occupation's massacres, the displacement of civilians and the policy of assassinations continue".
The police said Sunday's blast "was a terror attack involving the explosion of a powerful explosive".
"As a result of the explosion, a passerby was moderately injured," the police said, adding that authorities had ordered "an increase in alert levels and extensive searches throughout the greater Tel Aviv area".
It occurred shortly after US Secretary of State Antony Blinken arrived in Tel Aviv to push for a ceasefire in Gaza as fears grow of a wider, regional conflagration after more than 10 months of war, triggered by Hamas's October 7 attack on Israel.
