An Aboriginal man has died in a Melbourne prison just hours after returning from hospital.

the 32-year-old man was taken to St Vincent's Hospital on Wednesday morning for treatment.

He was then brought back to the maximum-security Port Phillip prison, where he died in the medical unit on Wednesday night.

A spokesperson from the Department of Justice and Community confirmed the man died on Wednesday.

"It is with great sorrow that Corrections Victoria acknowledges the passing of a prisoner at Port Phillip Prison," the spokesperson said.

"As with all deaths in custody, the matter has been referred to the coroner, who will formally determine the cause of death."

Premier Daniel Andrews said both the coroner and Corrections Victoria would conduct a full review into the death.

A statement was posted to the Corrections Victoria website late on Friday afternoon, saying: "We recognise that all deaths in custody have impacts on family members, friends, victims and the broader Aboriginal community, and we're working to ensure they are provided with the support they need."

Victoria's corrections system was heavily criticised during a recent inquest into the death of Aboriginal woman Veronica Nelson, who died alone in her cell despite repeatedly calling out for help.

A St Vincent's spokesperson offered the hospital's condolences and said it would comply with the coronial inquest.

Federal Attorney-General Mark Dreyfus told ABC Radio Melbourne he wanted all states to adopt uniform custody notification services.

He said national implementation of the support services would enable Aboriginal people in custody to speak to lawyers, family members and support services.

"We've made a commitment in the election to assist families with coronial inquests with the hope that if these deaths in custody are examined, we will learn more about how they can be prevented," he said.