The incident happened around 2.10pm on Sunday (May 10) on Marshall Avenue.
The Belgian Malinois, which is believed to have come off its lead, bit three adults and a four-year-old child.
All have received treatment at hospital with injuries that are not life-threatening.
A 15-year-old boy, a 34-year-old man and a 36-year-old woman, have been arrested on suspicion of being in charge of a dog dangerously out of control causing injury and are being questioned in custody.
Officers have seized the dog while the investigation is ongoing.
T/Inspector Mike Dalton, from Middlesbrough response, said: “Once the report was received, officers swiftly attended to the area and the dog was located and seized.
“As part of the investigation, three people have been arrested and will be questioned while officers establish what took place.
“I want to take this opportunity to appeal to anyone who has information or footage in the run to and during the bite to please get in touch by calling 101 or visiting the website quoting reference number 088568.
“If residents have concerns, I encourage you to please speak to an officer.”
Information can be provided anonymously by calling Crimestoppers on 0800 555 111.