A note -- "My mum's in doing the shopping, call her if I need anything" with a cell phone number -- was left resting on top of the baby's blanket as the child snoozed in the car.
A passerby spotted the child Saturday in a parking lot of a Pak'n'Save market in Porirua, north of Wellington, and snapped a photo, which quickly garnered outrage when posted on Facebook.
Police told the New Zealand Herald that no investigation is likely, since no one has lodged a complaint or come forward with information.
"We don't know who the people are, we don't know the phone number, we don't know where to start," said national police spokeswoman Anne Coughlan. "We would launch an investigation if we could but at this stage no one's come forward."
The man who took the photo said he waited with the child while others called the mother.
"We waited there for 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'."
Porirua police sergeant Justin Rakena said even if someone came forward, prosecution wouldn't be likely.
In most cases, he said, the best solution would be support for the parents from Child, Youth and Family Services.