The youngster, said to be just six weeks old, is now being treated for his injuries at the Royal Hospital for Sick Children in Glasgow after being transferred there from the Borders General Hospital at Melrose.
His name has not been released by police but he has been identified locally as Mikey Skelly, son of Lucy Donaldson and Michael Skelly.
It is understood that the tot was being looked after at the time by his 28-year-old mum’s sister Robyn and her partner, Chris Cooper, at their home in Hawick’s Burns Road.
The alarm was raised at around 4.30pm on Thursday, and both police and ambulance crews were sent to assist.
A Police Scotland spokesperson said: “Police were called to an address in Hawick following a report of a baby having been attacked by a dog.
“A baby boy has been taken to hospital, where he remains in a critical condition.
“Inquiries are ongoing.”
A Scottish Ambulance Service spokesperson added: “We dispatched one ambulance to the scene and transported a child patient to the Borders General Hospital.
“Our trauma team then airlifted the child to the Royal Hospital for Sick Children in Glasgow.”
The dog involved in the reported attack, said to be a Lakeland terrier, is understood to have been put down since.
No arrests have been made, but police say their inquiries are continuing following an investigation by a forensics team yesterday.