She bought the Ploughman's sandwich from the reduced section and ate half of it shortly after arriving home, leaving the other half in the fridge.
Ms Wood then reached for the remaining half some 30 minutes later, and noticed the "shocking" discovery in the packaging.
The health worker said: "My two-year-old wanted to taste it so I grabbed it from the fridge and when I saw it I started heaving - I was physically sick.
"It was a big caterpillar crawling out of the sandwich and out of the packaging."
"I never had a problem before so it was a shock for sure."
Ms Wood says she will "never buy sandwiches from supermarkets ever again" following the discovery of the caterpillar.
"When you have been at work all day and you get back at 7 you do not really want to cook, you just want a snack or something.
"I have never had a problem with sandwiches - I do get them quite a lot.
"But this is unacceptable.
"I will never buy sandwiches from supermarkets ever again because it has really put me off and I will just be thinking about that all the time."
The angry customer submitted a complaint to Sainsbury's on November 22 with a video of the caterpillar crawling on the sandwich packaging.
She added: "I am not bothered about the money really because it was only 54p.
"It is more about making people aware that this is happening and it cannot happen again.
"We just want them to make sure that everything is checked and washed properly.
"However I do expect some kind of compensation as well."
A Sainsbury’s spokesperson said: “Cases like this are extremely rare because we have processes in place to prevent them from happening.
"We are contacting Faye to apologise for her experience and we are investigating with our supplier.”