Acting premier Jeremy Rockliff said Mr Hodgman and his family were uninjured, and are all safe, “although understandably very shaken by the events.”

“The Tasmanian Government expresses its deepest sympathies to the victims, their families and friends, and to all of the people caught up in yesterday's horrific attack in Melbourne,” he said,

“I can confirm that the premier, who is currently on leave along with his family, was in the vicinity of the attack in Bourke Street, about 50 metres away, and was caught up in the rush to get away from the area.

“The Tasmanian Government is not aware that any Tasmanians were injured during the attack. Any Tasmanians who were in the vicinity of the attack and need support should call Lifeline on 13 11 14.”

Tasmanian Treasurer Peter Gutwein said earlier confirmed that the premier and his family were in the vicinity of what happened yesterday.

“First and foremost our thoughts are with those people that were affected and especially the families of those that have lost loved ones,” he said.

Among the four people killed were a man in his 30s, a woman in her 30s, and a young child.

Police confirmed the death of the fourth person on Friday night but are not releasing the age and gender of the deceased until next of kin have been notified.

A three-month-old baby girl who was taken to hospital by police officers is among six people with life-threatening injuries.

Three people are in a critical condition at the Royal Melbourne Hospital and two are in a critical condition at The Alfred Hospital.

An additional 23 people are being treated for injuries in Melbourne hospitals, including some who went into shock after witnessing the incident.

Police ended the chase by shooting the driver, who is injured but alive. 

The arrested man had an extensive history of family violence, drug and mental health problems. 

He had come to police attention because of some assaults in recent days, police said.