The boy, who was shot in the left thigh, was standing outside shops in Northern Avenue in Arbourthorne at around 3.45pm on Sunday, and was "an entirely innocent bystander" police have said.
Detectives revealed he was with three friends, aged 13, 15 and 16 when he was "caught in the line of fire of a targeted attack".
South Yorkshire Police have revealed a 25-year-old man from Sheffield has now been arrested on suspicion of attempted murder and possession of a firearm with intent to endanger life. He remains in police custody.
Enquiries are ongoing and anyone with information is urged to contact police on 101 quoting incident number 516 of 12 January 2020.