The 67-year-old woman was approached by a woman who reached into her bag, which was attached to her trolley by the handles, and took her purse from inside.
There was a small amount of cash in it, some bank cards and the victim's mum's wedding ring.
The cards were cancelled but one had already been used.
The incident happened at 12:10pm on Tuesday October 10 at the Aldi supermarket on Cuerden Way, Bamber Bridge.
A spokesman from South Ribble Police said: "We want to speak to the woman in the CCTV as part of our enquiries.
"We'd also ask you to be vigilant with bags and purses, particularly in supermarkets or places where you may be distracted.
"Always keep bags zipped-up and be aware of your surroundings and people around you. Let friends and relatives know this message as well and together we can help keep Lancashire safe."
Anyone with information should email [email protected] quoting reference SA1715965.