The toddler and his father were both taken to Vrinnevi Hospital to be treated for minor injuries after they were struck by the vehicle at a pedestrian crossing while out for a walk at 2am.
Police confiscated the vehicle and were later able to confirm that it had previously been reported stolen.
Father and son both fell to the ground when hit by the moped. The driver and his passenger also fell but quickly picked themselves up and fled the scene on foot.
Police are classifying the incident as a hit-and-run.
“We’re going to continue questioning witnesses to try to find the perpetrators,” police sergeant Gittan Gustafsson told Norrköpings Tidningar.
“It’s difficult with cases like this but maybe friends of the guys who stole the moped won’t be able to keep quiet and it will come out eventually,” she added.