The youngster was bitten during a police operation in Beighton yesterday afternoon.
A police dog had just been deployed by its handler to assist in the search for a wanted man when it bit the child.
After a police chase through the city suburb, the man was found hiding in a garden on Queens Road.
As officers approached him, he ran off again and a police dog was released.
During this phase of the operation three children ran past the police dog and one of them was bitten.
South Yorkshire Police said he was not seriously injured but the incident has been referred to the Independent Office of Police Conduct.
“Yesterday, just before 12:30pm, officers detained a man on Moss Way in Sheffield in connection to theft and attempted theft,” the force said.
“The man ran from officers and a search to locate him started.
“The National Police Air Service and a dog handler assisted the search.
“The man was found hiding in garden on Queens Road.
“As officers approached, the man ran and a police dog was released to detain him.
“The man stopped, and as the dog handler started to retrieve the dog, three children ran past. This resulted in a 10 year-old boy being bitten by the dog.”
“Enquiries will be carried out into the circumstances surrounding the incident.”