Police attended a property in Kilcreggan, Argyll, on April 13 after receiving reports a little boy had died.
The baby was flown to the Royal Alexandra Hospital in Paisley by air ambulance but could not be saved.
Police launched an investigation into the full circumstances surrounding the incident.
Yesterday, a 50-year-old woman was arrested in connection with the youngster's death.
A report has been submitted to the procurator-fiscal.
A Police Scotland spokeswoman said: "We can confirm a 50-year-old woman has been arrested in connection with the death of a 14-month-old baby in Kilcreggan, Argyll, on Sunday April 13."
The woman is due to appear at Dumbarton Sheriff Court next week.