Joseph McDonald appeared in custody in Melbourne Magistrates Court on Sunday after he was charged by homicide squad detectives over the death of his son Lucas McDonald five days earlier in a Melbourne hospital.

The 22-year-old handed himself in after Victoria Police put out an appeal to find him on Saturday in relation to his son's death.

A police statement said Lucas was admitted to Benalla hospital on Friday, October 25 with life-threatening injuries.

"He was then transferred to Monash Children's Hospital where he died on Wednesday, October 30," the statement said.

The court heard it was McDonald's first time in custody and was represented in court by a Legal Aid lawyer.

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The lawyer did not apply for bail, but requested McDonald be seen by a nurse while in custody, which was granted by the magistrate.

The court also heard McDonald was vulnerable in custody due to his age and appearance.

Police said in an earlier statement McDonald was last seen leaving Monash Children's Hospital on Clayton Road in Clayton, where his son had died on Wednesday, October 30 about 4.30pm.

It was believed he was travelling back to Benalla by public transport when the call was put out by police.

He was arrested and charged with one court of murder after he handed himself into a Melbourne police station about 6pm on Saturday.

McDonald was remanded in custody to reappear in the same court on Monday for a filing hearing.