A 29-year-old man and a 39-year-old woman were attacked by the dog – thought to be an American Bulldog type – during the incident on Newmarket Road, Cantley.
Both were taken to Doncaster Royal Infirmary following the attack.
Armed police were on the scene and the road was sealed off for around six hours as dog handlers battled to detain the dog.
A police spokesman said: “Their injuries are not thought to be life threatening.”
The dog was detained following the incident.
Officers attended a property on Newmarket Road, Cantley at around 7.15pm on Tuesday following reports that two people had been attacked by a dog.
An eyewitness, who did not want to be named, said he saw armed police on the scene and the road was sealed off for around six hours following the incident.
She added: “Newmarket Road had police blocked at both ends of the road and two ambulances attended.
“There were numerous squad cars, riot van dog handlers and armed police.
“The dog came out on the end of the dog handler’s pole and it was fighting against the handler.”
A spokesman for the ambulance service said paramedics attended at 7.09pm.
The incident comes after it was revealed almost 200 dangerous and illegal dogs have been destroyed on the orders of South Yorkshire Police in the past three years.