A man is now facing a charge of murder after a critically-injured baby died in an Auckland medical centre last month.

Today police said they had laid a murder charge as part of the homicide investigation into the death of a baby in Ōtara on May 23.

Counties Manukau CIB Detective Inspector Warrick Adkin said a 24-year-old man previously charged by police would now face an upgraded charge.

The man previously appeared in Manukau District Court on one charge of assaults child.

Due to suppression orders police were unable to comment further, said Adkin.

The upgraded charge comes a month after the infant was taken to Watford Medical Centre suffering critical injuries.

CPR was administered but the child was pronounced dead at the clinic.

A homicide investigation was launched into the circumstances of the death and a man was arrested the following week.