The fire at the Hanover block on Exeter Drive, Broomhall, was discovered in the bin store area at 1.45am.
An evacuation of the block was not needed.
Crews spent around an hour at the scene and ruled that the fire started accidentally.
Firefighters called to blaze at Sheffield tower block
Firefighters were called to a blaze at a tower block in Sheffield in the early hours of this morning.
By The Newsroom
Thursday, 4th January 2018, 8:10 am
Updated Thursday, 4th January 2018, 8:20 am