Tel Aviv's police chief David Tzur said the attack late on Friday took place at the entrance to the disco, called The Stage.
"A single terrorist exploded in a line of people waiting to get into the club," Tzur said.
Islamic Jihad, Hamas and al-Aqsa Martyrs Brigades - an offshoot of the mainstream Fatah movement - all have denied responsibility for the explosion.
Some Israeli security sources have suggested that the Lebanese Hizb Allah might be to blame for the attack, Aljazeera reported on Saturday.
Israeli police have set up checkpoints around Tel Aviv to capture a person who, witnesses say, was with the bomber before the attack, Aljazeera reported.
The Palestinian Authority, which has agreed to a ceasefire with Israel, was quick to condemn the attack.
"The Palestinian Authority will not be silent about this sabotage and it will pursue whoever stands behind this act and will inflict the required punishment," a statement said.
"We are against any operation which harms civilians, Israeli and Palestinian. This was part of our truce agreement with Israel at Sharm al-Shaikh," Nabil Abu Rudaina, spokesman for the Palestinian Authority, said.
Chief Palestinian neogiator Saib Uraiqat also condemned the attack, saying it undermined Palestinian interests, but appealed to the international community to ensure that Israel did not use the attack as an excuse to launch a major operation in occupied territories.
"We are against any operation which harms civilians, Israeli and Palestinian. This was part of our truce agreement with Israel at Sharm
Nabil Abu Rudaina
Palestinian Authority spokesman
"We are asking the international community to move immediately to ensure that Israel does not use this kind of operation as an excuse for aggressions against the Palestinian people," he said.
Sami Abu Zuhri, a spokesman for the resistance group Hamas, said the organisation was "fully observing the period of quiet as we told Abu Mazin (Mahmud Abbas) at our last meeting in Gaza".
"But the responsibility for this operation lies with the Israeli enemy because even though we are observing this period of quiet, the Israeli aggressions and crimes are continuing."
A senior leader of the Islamic Jihad - another Palestinian resistance group - denied any role in the blast.
"Islamic Jihad is committed to calm in accordance with the understanding it has reached with President Abu Mazin. The Islamic Jihad has no knowledge of the attack in Tel Aviv," Nafidh Azzam said.
Several Palestinians have been killed over the past month after the truce came into effect.
Israeli Public Security Minister Gideon Ezra said Israel would take matters into its own hands unless the Palestinians bring resistance groups to heel.
US Secretary of State Condoleezza Rice demanded that Palestinian leaders find those responsible and "send a clear message that terror will not be tolerated".