A video of the packaging blunder was re-tweeted by the Welsh Conservative AM Andrew RT Davies after it had been posted by his daughter Sophie Davies.
In the original tweet, Ms Davies said: "Bit misleading don’t you think @Morrisons… chicken branded with the British flag yet if you look at the food labelling on the back it says the chicken is from Thailand?!"
The video shows Sophie picking up the £1.50 chicken fillets to show the Union Jack branded front but with the details showing the ingredients, including the origin of the chicken, on the back.
Mr Davies, who described the packing as shocking, said he felt the packaging was misleading consumers who wanted to buy British meat.
He said: "This is simply ridiculous from Morrisons and demonstrates why we need stricter food labelling guidelines right across Wales and the UK.
"To package and produce in full Union Jack glory when it has been produced in Thailand is misleading consumers and the small detail on the back of its true location is no cover or excuse.
"This is an insult to many hardworking farmers across Wales and it cannot be right that produce from outside the UK is marketed and sold in such a misleading manner. This chicken hasn’t just crossed the road, it’s come half way round the world!
"I’ve today contacted trading standards at Powys County Council and action must be taken to prevent such ’misselling’ in future."
It is unclear whether Ms Davies contacted the store before she took to social media, however other Twitter users have expressed anger at the mistake.
Twitter user @georgilenne replied to the video: "I could almost understand if it was ’produced in Thailand from UK chicken’ or maybe even ’prepared in the UK from Thai chicken’ but even then it would be ridiculous to label it British. ’From Thailand with Thai chicken’: no excuse at all. @Morrisons @RedTractorFood."
Fellow user @sallmell tweeted: "Such a shame as @Morrisons have been supportive of British food. This is outrageous…"
Meanwhile @HelenMathieu tweeted: "So maddening. Surely there is a law that covers misrepresentation at this level? Read the label yes, but this kind of thing just casts doubt on the integrity of food producers generally. Disappointing."
However the supermarket, which is known for supporting British food producers, said it was a mistake at the store.
The British packaging is intended to be used for whole chickens which are sourced from the UK and not the breaded fillets which were produced in Thailand.
A Morrisons spokesman said: "We’re sorry about this mistake. The mini chicken fillets in this video have been put in the wrong bag after being baked in store."