A "decent human being", father of twins and highly skilled Melbourne surgeon is dead after being punched for telling someone to stop smoking.

New Zealand-trained heart surgeon Patrick Pritzwald-Stegmann died overnight on Tuesday in The Alfred hospital, almost four weeks after the attack at the hospital where he worked.

The cardio and thoracic surgeon graduated from the University of Otago in 2002 with a bachelor of medicine and bachelor of surgery, The Age reported.

His distraught family on Wednesday asked for space and privacy while they digested the news and dealt with its aftermath.

"Our family is devastated by Patrick's passing," they said in a statement on Wednesday.

The 41-year-old husband and dad to twin girls was hit in full view of CCTV at the Box Hill Hospital entrance on May 30 after he asked someone to stop smoking.

He was rushed to the trauma centre at The Alfred where he eventually died.

"We are grateful for the compassion and support we have received from friends, colleagues and the broader community over recent weeks," his family said.

David Plunkett, CEO of Eastern Health which runs Box Hill Hospital, said he was an admired member of the senior staff, passionate patient advocate and generous teacher.

"Patrick not only leaves a lasting legacy as a surgeon but as a decent and genuine human being dedicated to the wellbeing of others," Mr Plunkett said.

Victorian Health Minister Jill Hennessy said he was a "fine father, husband and surgeon".

"Patrick's family know that the hearts and minds of Victorians are with them at this very difficult time," she said.

"It's a devastating course of events and one that people are deeply, deeply grieving about."

The Victorian government is now considering extra safety and security measures to further protect healthcare workers.

Epworth Eastern Executive Director Louise O'Connor says the surgeon was a friend to many staff.

"We will deeply miss his care, his inclusiveness and the warmth that he radiated on his ward rounds," she said in a statement.

Australian Medical Association Victoria president Lorraine Baker noted the surgeon's high level of skills.

Mill Park man Joseph Esmaili, 22, has been charged in relation to the attack and faced court earlier this month.

"Investigators will now await the results of a post-mortem before reviewing charges," Victoria police said in a statement.