A 37-year-old woman has been charged with murder following the death of a two-month-old baby girl and the serious injury of her twin sister.

Police said the infants, of Coburg, were taken to the Royal Children's Hospital on April 26, where one died and the other was treated for serious injuries.

The woman, formerly of Coburg but now living in Brunswick, has been charged with one count of murder, one count of attempted murder and one count of intentionally causing serious injuries.