A three-month-old baby is in Starship hospital in a critical condition, and the man alleged to have caused the injuries will stay behind bars - for now.

The 34-year-old, who was granted interim name suppression today in the Masterton District Court, faces charges of wounding the infant with intent to cause grievous bodily harm.

The baby remains in a critical condition in Starship children's hospital.

Police were called to an incident at a residential address in Masterton on Thursday night where the baby was found with critical "non-accidental" injuries before being rushed to hospital.

Police conducted scene examinations at two Masterton homes and in one vehicle.

Officer in charge Barry Bysouth said police were investigating the alleged assault while also focusing on supporting the baby's family.

"This incident is traumatic for all involved. An investigation is underway and police are working hard to determine the circumstances of the [alleged] assault," Bysouth said.

"An equally important focus for the investigation team is the support of the whānau and baby."

He said the co-operation of the whānau, friends and the wider community was vital to the investigation.

Judge Barbara Morris granted interim name suppression to the accused and remanded the man in custody to appear next on July 7.

Judge Morris said the charges were surrounding the issue of a "very vulnerable young baby".