Melbourne car deaths: Family mourns 'perfect little baby'

The parents of a three-month-old boy killed in an allegedly deliberate attack by a motorist in Melbourne have paid tribute their son.

Matthew and Nawwar Bryant said Zachary, a "loving, happy, and perfect little baby", was the light of their lives.

"He leaves us with the best three months and 14 days of wonderful memories spent in this world," they said in a statement.

A man has been charged with five murders over the incident on Friday.

Dimitrious Gargasoulas, 26, was remanded in custody on Monday to face a court hearing in August.

Police allege he deliberately drove a car into pedestrians in Bourke St Mall in central Melbourne, killing five people and injuring 37 others.

Three of those killed have been identified as Thalia Hakin, 10, Jess Mudie, 22, and Matthew Si, 33. Another victim, a 25-year-old man from Japan, has not been named.

Zachary's two-year-old sister, Zara, was also injured in the incident and remains in a stable condition.

"Zac, Mummy and Daddy love you very much, and always will," the Bryants said, as they released photos of their two children.

Thousands of mourners attended a public vigil in central Melbourne on Monday night.

The city's Lord Mayor, Robert Doyle, thanked the crowd for its support following "an unthinkable act".

"Melbourne is our home," he said. "When it happens to one of us, it happens to all of us."