Kayley Asher, 25, was attacked by Allitt while being treated at Grantham Hospital as a baby.
She received £11,500 compensation but social security officials say she failed to notify them of this and must return benefits she has received.
Her parents, Alan and Sharon, say they have "no intention" of giving the money back and are prepared to go to prison.
Miss Asher, from Grantham, received an Employment and Support Allowance (ESA) for five years because she is unable to work and also a £120-a-week disability allowance.
Her parents said they used that money for her day-to-day care and were given the £11,500 in compensation when she turned 18.
However, the Department for Work and Pensions (DWP) says she failed to declare the payout when applying for the ESA, which is a means-tested benefit.
"We have never hidden the fact that Kayley had this money," said Mr Asher.
"We always believed that compensation was for her future. It was awarded because she needs special care."
Allitt was given 13 life sentences in 1993 for murdering four children and attacking nine others while working as a nurse at Grantham Hospital.
It is believed she injected 13-month-old Miss Asher with air under her armpit, causing her to have two heart attacks.
"The murderer had a go at her once and now the DWP are causing Kayley pain. It is totally wrong," said Mr Asher.
"We have no idea what the future holds for us.
"With a sum of money her future is secured if anything happens to her mum and I."
He said they intended to appeal against the DWP's decision and would risk going to jail.
A spokeswoman for the DWP said: "It is essential that claimants declare their income and savings accurately. This is to ensure that support is targeted at the people that need it most."
She said other non-means tested benefits were available to Miss Asher.
A woman left brain damaged by killer nurse Beverley Allitt has been ordered to pay back £23,000 in benefits.