Both women are said to have made a grab for the 18lb bird in Barry's Morrisons store in the Vale of Glamorgan, and after a tussle one of the shoppers walked off with it in her trolley.
But in the car park later, the younger woman who lost out on the frozen turkey shouted out that she hoped it got burned on Christmas Day.
The other woman is said to have stormed over and allegedly pulled out clumps of her hair.
A security officer at the store which only opened on the edge of Barry's docks in October said: "The customer came back into the shop in tears with clumps of her hair pulled out.
"She was shocked and very upset."
Police were called to the supermarket in Barry after the alleged attacker - a woman in her late forties - drove off.
A statement was taken from the injured shopper, 33, and police studied footage from the store's security cameras.
Inspector Phil Williams of Barry Police said: "We are investigating a complaint from a woman shopper which stems from a row over a Christmas turkey.
"The two women met up in the car park 20 minutes later and the woman who lost out on the bird said she hoped she burnt it on Christmas Day.
"An alleged assault took place and the woman had some of her hair pulled out.
"Whatever happened to peace and goodwill at Christmas?"
Police are appealing for other shoppers who saw the incident to come forward. Witnesses are asked to contact Barry Police Station.
A spokesman for Morrisons said as the police were involved in the case, they felt it was inappropriate to comment.