Harry Harper died from his injuries after the pet bit him just once while he was staying at his grandparents' home.
A statement released by Harry's distraught family today said: "As a family we are absolutely devastated by Harry's death and have no words to describe the loss we have suffered.
"At the present time we have no wish to speak publicly about yesterday's events and would ask that we are left in peace to grieve and begin to deal with our loss."
Harry's mother Mikayla, 19, was staying with her parents, Gordon Bell, 42, and Teresa, 40, in Ketley, Shropshire, when the attack happened.
Part-time model Mikayla, 19, gave birth to 7lb Harry on November 12.
A police spokesman said officers were awaiting the result of a post-mortem examination, and have launched an investigation to establish the precise circumstances of the death.
Initial indications however, suggest that the boy died as a result of a dog bite, police said.
The spokesman said: "Police and ambulance were called to an address in Ketley, about a young baby that was unwell.
"He was taken to the Princess Royal Hospital in Telford by paramedics but died soon after.
"As in all cases of the death of a young child, West Mercia Police has launched an investigation to establish the exact circumstances."
It is understood that the dog has been put down.