Concerned passers-by called the police after spotting the heavily sweating child in an Asda car park in Burgh Heath, Surrey, with no sign of the mum.
Paramedics and police arrived as the store put out public announcements.
Witnesses said the smartly dressed mum, in her 30s, casually returned and said she had nipped in to get baby milk She had several bags of shopping which she loaded into her black BMW.
A source told The Sun: "Officers took her to another part of the car park to have a word.
"Judging by the amount of shopping in her trolley she had been in the store for a long time."
One witness said: "The baby was dripping in sweat. You hear about people stupidly leaving dogs in hot cars, but you wouldn't have thought anyone would be silly enough to leave a baby.
"Crowds of people were around her car but the mum didn't seem to understand what all the fuss was about."
Police confirmed a woman was questioned over a child left in a car, and said: "The investigation is ongoing."
Thankfully, the paramedics did not need to treat the baby.
The case has echoes of tragedies that have happened in the States where babies have died after being left in hot cars.
More on Parentdish: is it ever safe to leave your child unattended in a hot car?