Ms Allan made the personal apology on behalf of the state government on Thursday in Melbourne's inner north.
The premier posted a picture online of the smoking ceremony after the event.
"Members of the stolen generations have never received an apology in person from the Victorian government. Until today," she wrote on Facebook.
"On behalf of successive Victorian governments and parliaments, I apologised to those children who were forcibly removed from their families.
Victorian Premier has made a private apology to members of the stolen generation.
"To the babies and children who grew up without knowing who they were. And the mums and dads who were left - sometimes for a lifetime - searching."
Former prime minister Kevin Rudd delivered an historic national apology to the stolen generation in February 2008 following the 1997 Bringing Them Home report.
Ms Allan said the state Labor government had been working with members of the Victoria's stolen generation since it came to office in 2014, and had listened to their voices.
"The apology is for that stolen generation," she told reporters in Shepparton on Friday.
"The attorney-general and I yesterday were joined by people in their 80s, people in their 50s who were part of that stolen generation who are still experiencing the grief and trauma of being torn away from their family at birth."
Opposition spokesman David Davis criticised the government for not inviting the media to cover the ceremony, declaring the apology should have been delivered in plain sight.
"Like many Victorians, I don't personally accept responsibility for things that have happened, indeed in many cases, before my family and perhaps your family were here," he said.
"But whatever statements we're going to make on behalf of the Victorian government should be done honestly and transparently."
In February, the Victorian parliament paused to hear Ms Allan offer a formal apology on behalf of the state to victims of historical abuse and neglect in institutional care.
Victoria Police Chief Commissioner Shane Patton also made a series of mea culpas over the force's mistreatment of Indigenous people at the state's truth-telling inquiry in May.
Ms Allan said her government was guided by the lived experiences of stolen generation members when deciding to hold the apology behind closed doors.
"They absolutely deserve the respect to be able to determine the safe, appropriate way that that apology is delivered," the premier said.
The surprise state apology came a year on from the federal voice to parliament referendum suffering a resounding defeat.
Though Victoria recorded the highest 'yes' vote of any state at 45.85 per cent.