Around 40 firefighters battled the blaze, which was brought under control about 6.15am.
It is unclear what caused the fire. A media spokesman said it was too early to tell if it was suspiciously lit.
Teachers and the current and former school principals of Sandringham Primary School are now surveying the damage and planning contingencies from a scout hall across the road.
School mum Ella Pigott said after hearing sirens at 4.30am, she woke up to video of the blaze in Whatsapp messages from other parents.
She said her two daughters Alexia and Jasmine, aged 6, were distressed when they realised their former classroom had been destroyed in the fire.
“It’s just devastating what’s happened. It’s not just a school, it’s a part of our family,” she said.
“When you peer through their old classroom, you can literally see out the other side, there’s nothing left of it. They got quite upset about it.
“Alexia’s immediate thought was as what happened to their class pet, which is a stick insect.”
Ms Pigott said the many pupils on scene were already discussing bake sales and fundraisers to rebuild the destroyed building.
No one was injured, and the building was empty at the time of the blaze.
Around 500 pupils attend the school, which at 165 years old is one of the state’s oldest primaries.
Crews are now expected to remain on scene for a significant amount of time, in order to extinguish hot spots ahead of the warm weather expected on Saturday.
Local resident Deb Ford said when she woke up on Saturday morning, she looked out her bedroom window and saw “huge flames leaping up in the air”.
“I thought I was dreaming, or having a nightmare. There was a huge amount of embers and sparks and explosions, it was quite dramatic,” she said.
“It’s the old part of the school that’s been ruined. I have three sons, they all attended class in that part. Everyone here is quite upset.
“The main things is that nobody was hurt … but there are a lot of sad people and young families, the school only started back yesterday.”
Ashleigh McMillan is a breaking news reporter at The Age. Got a story? Email me at email@example.com