The 40-year-old from Milan, who was also on holiday in the northern Italian region, is now facing legal action, La Stampa reported.
A passer-by asked the child where her mother was, at which point she pointed to a nearby bar, the newspaper said.
“It was just a joke, I wanted to play a game,” the mother told the woman, who in turn called the police.
Authorities in the town of Santa Margherita Ligure did not share the holidaymaker’s humour.
The mother is now being investigated for exploitation through begging.
A local child welfare court is also assessing her ability to look after her daughter, La Stampa said.