Two 12-year-old Aboriginal boys are in hospital with serious injuries after a man allegedly chased and struck them in a ute in Mildura last week, prompting outrage from community members.

Andrew Brien, 57, from Gol Gol in New South Wales, has been charged with four counts of reckless conduct endangering life, dangerous driving causing serious injury, driving in a dangerous manner and/or speed, and intentionally causing injury after he allegedly followed the two 12-year-old boys through a pedestrian-only mall in the Victorian town.

Both boys, who National Indigenous Times has confirmed are Aboriginal, were struck and sustained upper-body injuries before being hospitalised on Thursday evening.

One of the boys was flown to the Royal Children's Hospital Melbourne in a serious condition.

"Police will allege the man, driving a Ford Ranger Utility, was involved in a collision with two 12-year-old boys who were riding a motorised bike in the mall," Victoria Police said.

Mr Brien did not apply for bail at Mildura Magistrates' Court on Friday and will face court again this week.

On social media, Gellung Warl, the Aboriginal new governance structure in Victoria, referenced the incident and said, "Enough is enough."

"We are deeply concerned about the [alleged] attack on two children in Mildura," they wrote.

"Our strength and support is with the families and communities in the North West affected at this time. If you're mob living in Victoria, it's important to take care of each other and reach out for support if you're struggling."

The incident was also raised during Melbourne hearings of the Senate inquiry into racism towards First Peoples on Friday.

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