Clare Stobbart, a childminder who keeps five guinea pigs in a two-tier pen in her garden in Rathlin Close, discovered the incident this morning (Tuesday).
She said: "It's a miracle they have survived.
"I just cannot comprehend why someone would do such a thing. We have all been in tears here."
Clare said she first became aware of the incident this morning and said: "One of my little boys who I childmind, he said he could see something black in the cage.
"So I go out to have a look and thought, I don't know what that could be, I thought it might be a rotten pumpkin."
Clare said she started to worry and said she could not think straight and was beginning to feel sick as she tried to work out what had happened to her guinea pigs' pen.
She said: "I didn't understand and then I found the firework.
"It's not in there by accident, it's a completely enclosed cage."
Clare has reported the incident to the police, who said: "Between 11pm last night and 7am this morning the unknown offenders got in via a garden gate and placed a lit firework inside the guinea pig cage.
"The cage has been damaged and the guinea pig was covered in black ash but luckily seems uninjured."
Clare said she thinks the firework looks like a rocket and was put in the cage sometime overnight.
She said: "They have come into the garden. I don't know how they did it without us knowing.
"They have put that in there with the intention of killing them.
"I cannot believe the whole thing didn't go up."
Clare said the material beds for the guinea pigs have burnt and the pen is damaged, so she will have to replace the lot.
She has also had to move the guinea pigs inside which has been a squeeze when she has four children to child mind and her own two daughters, aged six and 17.
Clare said the whole thing has made her think fireworks should be banned from public sale.
She said: "I feel sick, I think it really needs to happen. They should just be for public displays."
She is also hopeful that the offenders might get caught and said Corby Council were reviewing CCTV of the area to see if they can trace the offenders.
Clare said: "What will they do next? People who hurt animals tend to go on to hurt humans. It's scary that anyone thinks to do such a thing."
A police spokesman said anyone with information should call 101.