The Jerusalem Post reported the elite unit was invited to celebrate a party for one of its soldiers, and stood at the entrance to the stage club when the bomber detonated the explosive device he was carrying.
Earlier, the platoon commander, Eran Cohen, told Army Radio (Gali Tzahal) that virtually all the casualties of the bombing were members of his unit.
"There were 13 of us there. All the fatalities are from our unit. Many more were wounded." Eran called the unit's soldiers "the best of the best, Israel's elite".
Earlier, the Israeli media had reported that all those killed and injured in the blast were civilians.
"In five years, none of our troops were wounded. It's ironic that we were hit so hard ... Just before a party"
Platoon commander Eran Cohen
"In the past five years of this war, we have carried out virtually every single mission in the [Palestinian] territories and underwent nearly every kind of attempted attack.
"In five years, none of our troops were wounded. It's ironic that we were hit so hard in one explosion on a Friday night in Tel Aviv. Just before a party," Eran said.
Israeli undercover units have assassinated hundreds of Palestinian political and resistance activists during the Palestinian al-Aqsa intifada against Israeli occupation, which started in September 2000.