The baby was presented to the Royal Hobart Hospital with "critical injuries" after an alleged assault on the morning of December 1.
Tasmania Police today confirmed the baby died in hospital on Friday.
A 25-year-old Warrane had his charge upgraded to murder after he was previously charged with grievous bodily harm.
"Our condolences are with the family and loved ones of the baby," Tasmania Police said in a statement.
The man is expected to re-appear before Hobart Magistrates Court today.
An investigation into the incident is ongoing.
