There had been no report of any casualty or any injury so far even as the flames were noticed around 3 pm, eyewitnesses said.
They said the black smoke and flames were noticed in a flat on the 16th floor of the Diamond City Housing Complex.
The residents of the flats were alarmed and they were seen coming out from the clutches of apartments.
State fire brigade minister Sujit Bose rushed to the spot where firefighting men were seen engaged in dousing the flames.