The thieves struck yesterday at 9.30am, at the Sainsbury's car park in Halifax, near the recycling area.
Two men approached the 39-year-old woman, and threatened her before stealing the car keys.
The woman had just locked the car and her young child was inside the vehicle when the thieves struck.
The two men fled with her keys in another car, believed to be a silver Ford Fiesta, in the direction of Queensbury.
Officers arrived on scene and force entry into the car to rescue the child, who was not hurt.
Detective Inspector Gary Stephenson. of Calderdale CID, said: "Clearly this has been an incredibly frightening and traumatic experience for the victim and her young child, who were thankfully un-injured. They are being supported by specially trained officers.ã€€
"There will have been a number of people visiting the Sainsbury's on Thursday morning, and I would appeal to anyone who was there around the time of the incident and parked near to the recycling centre who may have seen anything suspicious, or witnessed the incident itself to come forward.ã€€
"I would also appeal to anyone who may have seen a silver Ford Fiesta travelling towards Queensbury in the time after the incident, or who may have seen a vehicle matching the description in the Queensbury area to speak to police. Enquiries are ongoing."ã€€
Two men, in their thirties, from the Bradford area, have been arrested in connection with the incident and remain in police custody.ã€€
Anyone with any information is asked to contact Calderdale CID via 101 quoting 357 of Dec 1. Information can also be passed anonymously to the independent crime fighting charity Crimestoppers on 0800 555 111.