Laura Arber said she made the discovery in at least two of the 20 nuggets she had bought for her children from the fast food branch in Aldershot, Hampshire, yesterday.
The 32-year-old had taken three of her four children to the restaurant to pick up the order before they headed back to the family home to enjoy their meal.
As the family sat down on the sofa, Laura says she suddenly noticed Maddie, six, having difficulty eating before claiming to find parts of a blue disposal face covering.
She said: 'My little daughter just started choking and I put my fingers down her throat to loop it out there was just blue with the sick. I thought what on earth is this?
'I didn't even think it could be the chicken nugget but looked over at the box and all you could see was this blue coming out of another chicken nugget in the box of 20.
'And the mask is cooked into it, like a part of the mixture and it's clearly a mask. You can see the seam and how solid it is in there.'
After speaking to the branch on the phone Laura headed down to the store to speak to the manager and claims she was told that the nuggets were not cooked on site.
Laura claimed she did not receive an apology and was shocked that the restaurant did not stop serving nuggets.
The mother added: 'And the worst thing was that they carried on serving them. Before I left I said: 'Are you going to keep serving them?'
'And they were carrying on serving them and that was the big thing for me. I just couldn't believe the way the management were handling it.
'What if I had walked out of the room and my daughter had choked? She could have died. It's a split second thing.
'And I am just thinking, we have just come out of a pandemic and there is a face mask in my child's chicken nugget.'
Laura's son was born in intensive care and she stayed in accommodation provided by Ronald McDonald House Charities UK for families whose children are very ill in hospital.
She said she had always held the company in high esteem because of the way they helped her but said her experience yesterday left her feeling bitterly disappointed.
A McDonald's spokesperson said: 'We are very sorry to hear about this customer's experience.
'Food safety is of the utmost importance to us and we place great emphasis on quality control, following rigorous standards to avoid any imperfections.
When the matter was brought to the attention of our staff, we apologised, offered a full refund and asked the customer to return the item so we could further investigate the matter and isolate the affected product.'