The 56-year-old was arrested following the death of Stafford Garner, who was found by paramedics in his home in Monsal Street, Thurnscoe, at around 4.40pm on Thursday, April 2.
He was taken to hospital where he remained in a critical condition until his death three days later.
A post mortem examination provided the preliminary cause of death as a head injury.
The latest suspect has been bailed pending further enquiries.
Four other men, aged 28, 29, 31 and 41, are also on bail after previously being arrested on suspicion of murder.
Detective Inspector Rob Platts said: “We appreciate that many people will have been indoors due to the government guidance around the pandemic, but we’d like to hear from anyone who knew Mr Garner or anyone who lived locally who may have heard or seen anything suspicious.”