Emergency services were called to Burman Road, Wath, at about 8.05pm following reports that shots had been fired outside of a supermarket.
The victim, a 29-year-old man, was found with a gunshot wound to his back. He was taken to hospital for treatment and has since been discharged.
Detective Inspector Denise Booth said: “The 27-year-old man was arrested at the scene, on suspicion of attempted murder. He remains in custody where he will be questioned by officers.
“There will be extra policing resources in the area today, carrying out detailed enquiries to establish the exact circumstances around what happened and provide reassurance to local residents.
“Please do speak to them if you have any concerns or information. Please call 101 quoting incident number 786 of January 10 if you can help. You can also pass information to Crimestoppers anonymously on 0800 555111.”