The baby was spotted in the car park at Porirua Pak'nSave in Wellington,New Zealand, around 9am on Saturday, according to reports.
One passer-by told The New Zealand Herald: "[The note] was written from the baby's perspective, and it said 'My mum's in doing the shopping, call her if I need anything', and it had the cellphone number.
"We waited there fore a little bit, wondering if the mum was just going to be two seconds and come back. And my wife said, 'I'm not going in without someone being here with the baby'."
Other witnesses called the number on the note.
Police said the incident had not been reported so it would not be investigated.
"We don't know who the people are, we don't know the phone number, we don't know where to start," said spokesman Annie Coughlan.
"We would launch an investigation if we could but at this stage no one's come forward."