The three-month-old baby killed in the Bourke Street rampage on Friday has been identified as Zachary Bryant.
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.
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 on Monday afternoon, confirmed that a Japanese national in his 20s also died in the tragedy.
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.