The woman, in her early 30s, lives near Geelong. She wrote a "lengthy sales pitch" that included photographs of her son and daughter, both aged under 10.
Several people placed bids on the sickening auction, which has alarmed authorities.
Detectives from the segxwal Offences and Child Abuse unit were alerted to the internet page by a horrified member of the public.
The page has been taken down and the woman's children could be taken into permanent care.
Victoria Police has decided not to press charges against the mum, who claims the act was a joke.
However, police sources told the Sunday Herald Sun they were disturbed by the incident and in particular the genuine bidders who tried to obtain the children.
Officers continue to probe the people who bid on the children and the Department of Human Services is continuing its investigation into the family.
"Investigators from Geelong were notified last week that a mother was trying to sell her two children on eBay," a Victoria Police spokeswoman said.
"Photos of the children, a boy and a girl both aged under 10 years, were included in the sales pitch."
The page was posted on Wednesday and was active until late morning the next day.
"The mother wrote a lengthy sales pitch that was very interesting reading," a police source said.
"She said the page was created as a joke, but what worries us is the people bidding on the auction. Who knows who these people are. They could be paedophiles or anyone. It's extremely disturbing."
Officers immediately contacted eBay, which took the page down within two hours. Auction site staff then provided detectives with full details of the woman.
She faced charges under section 493 of Failing to Protect Child from Harm, which carries a maximum sentence of 12 months in prison.
But officers accepted her plea that it was a joke.
However, they have referred the matter to the DHS, which is still investigating the family.
A spokesman said it was possible the children could be taken into care.
"If there is a serious threat to the children's wellbeing and the situation is so bad that the only safe option is for them to be taken from home, then that is definitely a possibility," he said.
"This action could attract the attention of the wrong sort of people, whether it was a joke or not, and the family need to understand the risks and receive advice around that.
"We will continue to engage with the family and assess if there are any underlying problems.
"We need to get to the bottom of why she did this.
"Is there a mental illness, is the mother not coping or was it simply a joke? I don't recall another case like this."
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