Police Scotland said officers were made aware of an injured baby at Royal Aberdeen Children’s Hospital at about 12.30am on Wednesday 11 June.
The force said the boy died a short time later and his family had been made aware.
Sky News understands the incident in which the baby suffered the injuries did not take place at the hospital.
A Police Scotland spokesperson said: “The death is being treated as unexplained and enquiries are ongoing to establish the full circumstances.
“A report will be sent to the procurator fiscal in due course.”
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NHS Grampian said it would be inappropriate to comment on an ongoing police investigation.
