The body of the 56-year-old was discovered at a property in Shirley Road, Hexthorpe, at about 17:00 GMT on Monday, South Yorkshire Police said.
His death was being treated as suspicious, the force said. Post-mortem tests are due to take place later.
The suspect remains in police custody. Police said extra patrols would take place “to reassure the community”.
“Efforts are ongoing to locate the man’s next-of-kin and a scene remains in place in Shirley Road as officers conduct further enquiries,” the force added.
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