Officers were called to reports of a fight inside a block of flats in Water Slacks Close, Woodhouse, at 5:38am this morning.
A witness said one male was covered in blood and had been hit over the head with a glass bottle.
He was taken to hospital where his injuries are believed to not be life threatening.
The other male involved in the fight was arrested by police.
South Yorkshire police said a cordon was in place while they carried out their investigation.