The building collapsed at around 1:30 am, trapping the 17-year-old girl under debris, a police official said.
The girl was later taken to a nearby hospital, where she was declared brought dead.
Other occupants of the building managed to come out safely, the official said.
A Kolkata Municipal Corporation official, after an inspection of the site, said the building had been declared as condemned, but the occupants refused to vacate.
The building was being razed by KMC personnel.