The affected products have a best before date of October 2020 and carry one the following codes on the back of the pack: L9208 W V124; L9208 X V124; L9208 Y V124; L9208 Z V124.
No other batch codes or other Birds Eye products are affected.
The frozen foods giant said in a recall notice: "A small number of packs produced over a short time period may contain small pieces of clear plastic. Birds Eye apologises for the inconvenience to all our consumers."
People who have bought the products with the above codes are being warned not to eat the nuggets, but instead return to the store where it was bought for a full refund.
Alternatively, customers can send the batch code on the packaging to Birds Eye Limited Freepost ADM3939 London SW1A 1YS.
Notices will be displayed in all stores that are selling the product.