Relatives of Harry Harper, who died in hospital in Telford, Shropshire, said in a statement: "As a family we are absolutely devastated by Harry's death and have no words to describe the loss we have suffered.
"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 was pronounced dead after being taken to Telford's Princess Royal Hospital from a semi-detached house in Woodside Road, Ketley, Telford, yesterday morning.
Police have confirmed that "initial indications" suggest the infant died as a result of being bitten by a Jack Russell.
Detective Chief Inspector Neil Jamieson, of West Mercia Police, said: "Our investigation is ongoing but it appears that the baby died as a result of a dog bite.
"The dog in question was a family pet -- a Jack Russell -- and this animal has been put down.
"A post-mortem will be taking place to establish the exact cause of this baby's death but at this stage it does appear to be a tragic accident."
Mr Jamieson added: "I would like to ask the press to report this incident as sensitively as possible as the family involved are devastated by their loss.
"With an investigation ongoing, there is no further comment I can make on this matter apart from to say that all our thoughts are with the family of the baby at this extremely sad time."
Police and paramedics attended the property in Ketley shortly before 8am yesterday, but Harry died soon after being admitted to hospital.
His death has been reported to the local coroner and West Mercia Police are carrying out an investigation to establish the precise circumstances.
Residents in the local area were reluctant to speak to the media about the tragedy, which is reported to have happened while Harry and his mother were at her parents' home.
One neighbour, who declined to give her name, told reporters: "It's very, very sad.
"Losing a baby must be heart-breaking. However, it happens and they need to be left to grieve."