Police and ambulance crews were called to an address in Brixham, Devon, just after 11am on Tuesday, following a report that a child had stopped breathing.
The infant was taken from the house in Pine Close to Torbay Hospital, where he was later pronounced dead.
A 30-year-old local woman was arrested in connection with the incident and is in custody at Torquay police station, awaiting interview.
A Devon and Cornwall Police spokesman said: “Inquiries are ongoing to establish the circumstances of this tragic incident and the cause of death.
“The next of kin are aware but at this stage the name of the child is not being released and the press is asked to respect the privacy of the family at this difficult time.”
Detective Inspector Steve Parker said: “The investigation is at an early stage and forensic examinations of the scene are ongoing.
“This is a tragic incident and our thoughts are with the family during what must be a terrible time for them.
“A dedicated team of detectives are working on the inquiry and will be working closely with our partner agencies to establish the exact circumstances that led to this death.”
The arrested woman is understood to be the boy’s mother.