Five adults and two children were led to safety from Nauls Mill House in Coventry after the blaze broke out at about 8.50pm on Saturday.
Another six people, including a child, were able to get out by themselves and nobody was seriously hurt.
West Midlands Fire Service said a further 19 residents were moved to a nearby library.
Crews from Coventry, Solihull and Birmingham were called to the 16-storey building on Middlesbrough, with 75 firefighters arriving in 13 fire engines.
The fire was put out just after midnight and an investigation into the cause has been launched.
West Midlands Ambulance Service said four people were assessed at the scene and treated for minor injuries.
The fire service said crews arrived within two minutes of getting the call and described the blaze as “severe” and “very challenging”.
A spokesman said the fire had spread from the flats to a balcony above.