Eleanor Bryant, 43, was killed when an out-of-control truck crashed into the Macedon Ranges Montessori Preschool's playground, northwest of Melbourne on Monday.
The speech pathologist died at the scene and a three-year-old boy was taken to the Royal Children's Hospital.
Ms Bryant's family said there is an enormous hole in their hearts and they will "miss her like crazy".
"She was the light of our lives: a cherished mother, wife, daughter and sister, and beloved by all her family and enormous network of friends," her family said in a statement.
"Her infectious smile, sense of humour and passion for life made her a joy to be around.
"There is an enormous hole in our hearts today."
The family thanked emergency services and the public for laying tributes as they requested privacy.
Dozens of bunches of flowers have been placed along the kindergarten's fence by mourners, including children with tears in their eyes.
Police are yet to interview the 68-year-old driver whose tanker veered off the road and ploughed into the kindergarten.
Victorian Police Commissioner Shane Patton said the driver remains under hospital observation and will be interviewed once he is medically cleared.
Mr Patton said it was still too early to confirm whether the driver suffered a medical episode.
"We're not going to rule anything in, and we're not going to rule anything out at this stage," he told ABC Melbourne Radio on Tuesday.
Police are yet to interview the driver whose tanker veered ploughed into a Victorian kindergarten. (James Ross/AAP PHOTOS)
In an emotional tribute on Tuesday, Nine's Today Show presenter Alex Cullen described his childhood friend as "a light that lit up every room."
"It does not surprise me one bit that Eleanor pushed those school kids out of the way yesterday to ultimately save their lives, she always, always put others first and was a great example to all of us," he said.
She was an accomplished speech pathologist who grew up in Coonamble in NSW's central west and leaves behind a husband, 11-year-old son and nine-year-old daughter.
Mr Patton described Ms Bryant as heroic after preliminary briefings indicated she moved multiple young children out of the truck's way.
"Just so brave, and the whole incident is an absolute tragedy," he said.
A boy hurt in the accident was treated for an arm injury, which ambulance officials said was not life-threatening.
Detective Senior Sergeant Christian Von Tunk said initial investigations indicated the truck lost control on a bridge about 120m from the pre-school.
The local basketball club said they are devastated by the loss of Ms Bryant, who was their equipment and uniform co-ordinator.
"Eleanor was the most kind, thoughtful and funny friend," the club's Facebook post read.
"She gave generously to her community and was committed to supporting the RCR kids to get onto the court. Most importantly, Eleanor was an amazing mum and wife."
McKenzie Water owner Alan McKenzie confirmed the truck belonged to his company.
"Our experienced 68-year-old driver is understood to have suffered a medical episode and remains in hospital ... we are doing what we can to support him and his family," he said.
Macedon Ranges Shire Council CEO Bernie O'Sullivan offered his deepest condolences and vowed to support those affected.
The crash comes less than two weeks after 11-year-old Jack Davey was killed and four other students injured after an SUV crashed through a fence at Auburn South Primary School in Melbourne's east.
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