The supermarket said its Just Cook Chicken Breasts with Piri Piri sauce carries Chicken and Bacon Lattice instead - which also has milk and wheat in the ingredients.
The pork, milk and wheat were not mentioned on the label, endangering the health of people with a food intolerance.
Eating the wrong meal by mistake would also alarm those who cannot eat pig meat because of their faith.
A Sainsbury's spokesman said: "It has been brought to our attention a small number of packs labelled Chicken Breasts with Piri Piri Sauce contain Chicken and Bacon Lattice which has cheese, wheat and pork that are not declared on the label.
"As a precautionary measure, we are asking customers who have purchased this product to return it to their nearest Sainsbury's store, where they will receive a full refund.
"No other products or date codes are affected by this issue, and we apologise for the inconvenience this may cause."
The Food Standards Agency (FSA) issued an 'allergy alert' over the dodgy food item, which comes in a 326g size with a 'use by' date of 24 January 2016.
It warned: "The product is a possible health risk for anyone with an allergy or intolerance to milk or milk constituents and/or an allergy to wheat or intolerance to gluten."
It added: "If you have bought the above product and have an allergy or intolerance to milk or milk constituents and/or an allergy to wheat or intolerance to gluten, do not eat it.
"Instead, return the product to the Sainsbury's store from where it was bought for a full refund."
Sainsbury's said it had contacted the relevant allergy support organisations, which will tell their members about the recall.
Its statement is being displayed on notices at store checkouts. No other Sainsbury's products are known to be affected.
Added the high street giant: "No other products or date codes are affected by this issue, and we apologise for the inconvenience this may cause."
An FSA spokesman added: "Sometimes there will be a problem with a food product that means it should not be sold. Then it might be 'withdrawn' (taken off the shelves) or 'recalled' (when customers are asked to return the product).
"Sometimes foods have to be withdrawn or recalled if there is a risk to consumers because the allergy labelling is missing or incorrect or if there is any other food allergy risk. When there is a food allergy risk, the FSA will issue an Allergy Alert."