Mayor Anibal Ibarra said that doors had been "locked with chains and padlocks" before one concert-goer set off flares and ignited the fire.
"If the emergency exit had been open, so many people would not have died," he told reporters on Friday.
Police arrested Umar Chaban, owner of the Cromagnon Republic club, who was questioned by a judge, a source at the Interior Ministry said. Charges were not immediately known.
Interior Minister Anibal Fernandez said most of the clubgoers were aged between 12 and 20, although others were under 10, as some Argentine nightclubs provide child care.
Fernandez blamed overcrowding and blocked emergency exits, lamenting that young revellers "were caught inside a death trap".
The head of Buenos Aires emergency services, Julio Salinas, said about 102 of the 889 injured were in a critical condition.
Some 18 police officers were among the injured. Bodies were lined up on the street as firefighters fought to put out the blaze.
"People fired the flares into the ceiling, which was made of cloth and rubber," 15-year-old Cecilia Arce said.
"The rubber started burning, but with few or no flames, making a terrible smoke that choked you, killed you, if you breathed it."
The spreading fire and smoke reduced visibility. "Suddenly, we couldn't see anything because of the smoke, and the fire spread to the stage area," another young man said.
Nearly all the victims of the blaze
The witnesses said a mad dash for the exits began, with hundreds of people pressing into each other.
Several people said an emergency exit was shut and that other entrances and exits to the club remained closed while smoke filled the venue.
They said many of the victims died because, in the confusion, they ran away from the exits.
"Many people were drunk, and instead of running toward the five exits, they ran to the two upstairs platforms where the bathrooms are located. There, they choked to death and were trampled," said Roberto Gutierrez, a waiter at a nearby cafe who ran inside the club to help the victims.
Condolences were sent by Pope John Paul II, Spanish King Juan Carlos and Queen Sofia, as well as the governments of Brazil, Chile, France and Venezuela, among others.
The federal government declared three days of mourning and Buenos Aires suspended all concerts, festivals and discotheques at the New Year.