An Adelaide woman has been charged with the murder of a nine-week-old baby earlier this month.

Police and ambulance crews were called to a Woodville home on December 5 after reports of an unresponsive infant.

Despite their efforts, the baby was pronounced dead at the scene.

A 40-year-old woman has now been charged with the child's murder and is expected to appear at a bedside court hearing on Friday after being admitted to hospital under the Mental Health Act.