Zachary's two-year-old sister Zara was also injured in the incident.

Their parents Matthew and Nawwar Bryant released a statement on Monday evening, remembering Zachary as a "beautiful, loving, happy and perfect little baby".

"On 20th January a man drove through Melbourne city, killing and hurting people, including our two-year-old toddler Zara and our three-month-old son, Zachary.

"Our beautiful Zara is in a stable condition, however Zachary, our son, did not survive.

"He was the most beautiful, loving, happy, and perfect little baby we were so lucky to be gifted with. He was the light of our lives constantly filling our days with smiles and laughs. He leaves us with the best three months and 14 days of wonderful memories spent in this world.

"Zac, Mummy and Daddy love you very much, and always will.

"We want to thank everyone who has helped us, comforted us and grieved with us. Your kind words really mean the world to us. We ask you to keep us and Zara in your prayers."

Zara remains at the Royal Children's Hospital in a stable condition.

Zachary was so severely injured, paramedics handed him to police at the scene, saying there wasn't time to wait for another ambulance to arrive to take him to hospital.

Police rushed the three-month-old to hospital in a patrol car. He died at the Royal Children's Hospital on Saturday night.

Five people were killed when a car drove through Bourke Street Mall on Friday afternoon, hitting 37 pedestrians.

The victims include 10-year-old Thalia Hakin, Melbourne father Matthew Si, 33, and Sydney woman Jess Mudie, 22.

The Japanese Consulate in Melbourne confirmed on Monday afternoon that a Japanese national in his 20s also died in the tragedy.

Jess Mudie was visiting Melbourne, where her older brother and his fiancee had recently moved, when she was struck by the car on Bourke Street.

Her twin sister Emily posted a smiling image of her sister online as the family released a statement on Sunday describing her as the "most badass" daughter and sister.

In their statement, Ms Mudie's family remembered her as cocktail-loving, smiling "bright bubble of joy", who was on the up as an insurance broker. Ms Mudie left Allianz Insurance last February to take up a role as a consultant for national insurance broker Marsh.

Matt Si had just finished having lunch with his wife Melinda in the city on Friday. They had parted to return to their respective offices when Mr Si was struck down.

"The family would like to thank everyone who helped Matt at the scene and did their best to save him," Melinda said in a statement.

Thalia Hakin, 10, attended Beth Rivkah Ladies College.

Her nine-year-old sister, Maggie, and mother, Nathalie, were also caught up in the horrific crush of pedestrians and are still in hospital. Nathalie remains in a stable condition at the Royal Children's Hospital.

Yeshivah-Beth Rivkah Schools college principal, rabbi Yehoshua Smukler, said Thalia was a well-loved student and friend.

"Our hearts are broken at the tragic passing of Thalia," he said. "Our deepest sympathies goes out to her family at this most difficult time."

The man alleged to have carried out the deadly rampage has been charged with five counts of murder.

Dimitrious "Jimmy" Gargasoulas, 26, refused to appear in Melbourne Magistrates Court on Monday because he was "unwell".

He was remanded in custody.

Donations for the immediate families of those killed can be made via the website www.vic.gov.au/bourkestreet.html

For urgent support, call Lifeline on 13 11 14. Witnesses and victims requiring support can also call the Victim's Support Helpline on 1800 819 817.