A 39-year-old man and a 16-year-old male have been arrested on suspicion of causing grievous bodily harm.
Police say they believed it was an isolated incident.
They added that it was not clear whether a gun or an air weapon was used. The rider of the motorbike was not injured.
The Northumbria force said there was no risk to the wider public although extra officers are in the area to provide reassurance.
Police cordoned off Hewitt Avenue, a street of semi-detached homes, and were carrying out house-to-house inquiries.
Ch Supt Ged Noble said: “I would like to stress that we do not believe that this incident is in any way linked to other incidents that we have had in the city where a firearm has been discharged.”
A mother from the road said a group of four or five children played on motorbikes locally but were well-behaved.
Brogan Connify, 21, said: “They are quite considerate for being such young kids. There have been times I have asked them to keep the noise down and they have apologised and moved.
“There’s nothing to cause this, no bullying.
“With it being such a small community, they have all grown up together, it doesn’t matter the age. This is a massive shock.”
Another resident, who asked not to be named, said there was a group of youngsters who legitimately rode motorcycles. He said people believed the boy was shot with an air weapon.