A 31-year-old man has been granted name suppression after being charged with murder of a 5-month-old baby.

The baby boy died in Wellington Hospital yesterday.

The man appeared in the Wellington District Court this morning, where he was granted interim name suppression until his next appearance in the High Court on July 4.

He did not apply for bail and was remanded in custody.

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Police say the man was known to the baby.

As well as the murder charge, police have also laid a charge of wounding with intent to cause grievous bodily harm, saying the offence took place between May 7 and June 4.

Emergency services were called to an Upper Hutt home on Monday this week, where the baby boy was found with serious injuries.

The boy was treated, including undergoing surgery, but died in hospital yesterday.

Police are now examining the home where the baby was found.

A police spokesperson said that they were unable to comment further as the matter was now before the courts.

One neighbour was not aware a baby had died.

"[We've] never had any trouble around here. It's a very good area," she said.

A man living next to the house where the baby was found said he had never met his neighbours, or spoken to them. He said the area was good and quiet.

Upper Hutt mayor Wayne Guppy said he was "angry and upset" at the news of the baby's death.

"I know the Upper Hutt community will be just saying 'why? Why do these things happen?'"

Guppy said the death was "unbelievable and yeah, absolutely tragic".

"These tragic events continually happen and it's an issue for the whole country. There's just no way in the world these events should be happening like they are."