Footage has emerged of the desperate panic as people frantically sought to flee the venue after someone apparently set off a pepper-type spray.
Dozens were also injured in the ensuing crush in the town of Corinaldo, on the central Adriatic coast, including 13 in a serious condition.
The ages of the dead teenagers – three girls and two boys – ranged from 14 to 16 and the woman, who had taken her daughter to the concert, was 39, police said.
Officials said panicked people ran for the exits of the Lanterna Azzurra (Blue Lantern) disco after a noxious substance was sprayed in the crowd at 1am local time (12am GMT).
Local reports suggest around 1,000 people were in the nightclub for a performance by the Italian rapper Sfera Ebbasta.
Images on social media show people hurrying from one side of the very dark club to the other. Rafaele Lerino, who was there with his 10-year-old daughter, posted on Facebook that the dancefloor inside was empty in 20 seconds.
The rapper said he was “deeply sorry” and sent his “love and support” to the victims’ families.
He added: “I don’t want to pass judgement on those responsible for this, but I’d like everybody to pause and think about how dangerous and stupid it can be to use pepper spray in a disco.”
Interior minister Matteo Salvini said there possibly was a “stink” that could have been ammonia or another substance.
He said there probably were “more people inside than was permissible”.
“People cannot die like this,” Mr Salvini said.
“We will find those responsible for these six broken lives, those who out of malice, stupidity or greed have turned a party night into a tragedy.”
The victims have been identified as: Asia Nasoni, 14; Daniele Pongetti, 16; Benedetta Vitali, 15; Mattia Orlandi, 15; Emma Fabini, 14; and Eleonora Girolimini, 39.
Shortly after the stampede, the fire service said “the cause may have been the dispersal of a stinging substance, the young people fled and trampled over each other”.
A teenage survivor told Italian media: “We were dancing and waiting for the concert to start when we smelt this pungent odour.
“We ran to one of the emergency exits but we found it blocked, the bouncers told us to go back.”
But Mr Salvini said the initial investigation “appears to knock down” the possibility that a fire exit had been blocked.
A fire brigade commander in the nearby town of Ancona, Dino Poggiali, said it was too early in the investigation to know if any safety violations might have played a role.
He said that when rescuers arrived, all the doors were open.