The tragic incident occurred in Guisborough, in the borough of Redcar and Cleveland, North Yorkshire.
The North East Ambulance Service and Cleveland Police were called to Derby Road, Guisborough, on Thursday morning.
Cleveland Police said: "Police were called to a property on Derby Road in Guisborough around 8.15am on Thursday by ambulance service colleagues who were in attendance at a medical emergency.
"Sadly, a short time later a baby was pronounced dead at the scene. A post mortem examination will be carried out in due course.
"Our thoughts are with the family of the child at this very difficult time. The family have asked to be left alone at this time to grieve in peace."