The 45-year-old is being held over an attack in which a 43-year-old was knifed in his chest in Gresley Road, Lowedges, at 5.45pm yesterday.
South Yorkshire Police said the stab victim's injuries are not believed to be life threatening.
He is being treated in the Northern General Hospital.
A police spokeswoman said: "At around 5.45pm yesterday, police responded to reports of a man with a suspected stab wound following an altercation on Gresley Road, Lowedges, Sheffield.
"A 43-year-old man sustained a stab wound to the chest and was taken to hospital to receive treatment. His injuries are not thought to be life threatening.
"Two men have been arrested in connection with the incident. A 43-year-old man was arrested on suspicion of affray, assault and driving whilst being unfit. He currently remains in police custody.
"A 45-year-old man was arrested on suspicion of assault.
"Officers are currently investigating the incident."
Anyone with any information should call South Yorkshire Police on 101.