The blaze broke out at around 11:00 pm (local time) at the Colectiv night club, where hundreds of people had gathered for a gig by rock group Goodbye to Gravity.
The interior ministry said 27 people had died so far, most of them teenagers and young people, while 162 injured were being treated in several hospitals in the capital.
Hospital sources said the death toll could rise as at least 25 people were in critical condition.
Witnesses quoted by local media described scenes of chaos when fireworks, let off as part of the show, set fire to a pillar and part of the ceiling.
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The crowd panicked as thick smoke engulfed the room, leaving people scrambling to escape from the underground club located in a communist-era basement.
"People were fainting, they were fainting because of the smoke. It was total chaos, people were trampled," witness Victor Ionescu told local television station Antena 3.
The bassist and singer in Goodbye to Gravity, who were playing a gig to promote their new album, were among those seriously injured, Antena 3 said.
Another witness, Alain Panduru, said the fire spread in seconds.
"People could not get out of the club because there was only one exit open and the stampede happened immediately," he told online news portal Hotnews.
Several media outlets reported that a second exit was closed when the blaze broke out.
Police have started an investigation and in the early hours of Saturday morning groups of sombre-faced officers were still sifting through evidence outside the club.
"It is a very sad moment for our nation," he said in a post on his Facebook page, expressing his "solidarity and compassion" for the families of the victims.