Queensland Police are investigating the death as suspicious, and a 35-year-old woman and a 37-year-old man are assisting detectives with their inquiries.

The baby, from the Logan district, was taken to Logan Hospital in the morning with life-threatening injuries before being transported to the Queensland Children's Hospital in a critical condition.

She died in the hospital on Tuesday afternoon.

Detectives from Logan Child Protection and Investigation Unit and the state crime command's Homicide and Child Trauma squads are investigating.