The Ministry of Social Development says a law that left a solo parent with only $576 of the $40,000 ACC payment she was supposed to receive is discriminatory.
But the government department can't stop enforcing the law until the wording of the Social Security Act is changed.
The announcement comes following a Human Rights Review Tribunal declaration on a landmark discrimination claim brought by former Waikato woman Maree Hennessy.
Hennessy was working part-time while receiving a sole parent benefit when she suffered an accident at work in 2000 which forced her to stop work completely in 2002.
It took until 2010 for ACC to accept liability to pay earnings-related compensation for the period 2002 to 2010.
When ACC finally accepted liability to pay earnings-related compensation for that eight-year period, it calculated it owed Hennessy more than $89,000 in backdated weekly compensation, before tax.
But because she received MSD payments over that period, ACC paid her only $576. The rest went to the MSD because of legislation that led MSD to deduct the ACC payment from Hennessy's benefit income "dollar for dollar".
The deduction of benefit income is known as abatement.
If the payment had come from a source other than ACC, Hennessy would have received about $40,000 once MSD had abated her benefit income for the period.
She complained to the Human Rights Commission in 2014 and brought a claim in the Human Rights Review Tribunal in 2017.
The tribunal cannot overturn the law, but declared that the legislation which requires the dollar for dollar abatement is inconsistent with the right to be free from discrimination.
The Attorney-General, on behalf of the Ministry of Social Development, did not oppose the declaration.
The declaration is only the fifth of its type since 2002. It is the first declaration to be made where the Government has conceded the case without a hearing.
Hennessy said the dollar for dollar abatement caused years of severe financial strain for her and her family.
"I was an injured, unemployed single parent, with almost no access to legal help, trying to fight a legal battle," she said.
"I felt I was being treated unfairly and I took offence when it became obvious that governments have been gaining from the losses of injured beneficiaries over the years.
"If the law treated earnings-related compensation as 'income' then there would be no issue. I think people would be surprised if they realised a beneficiary's working income is not protected."
She now wants Parliament to change the law to ensure that beneficiaries have the same access to their ACC entitlements as others.
Hennessy was represented by Greg Robins, a senior solicitor at the Office of Human Rights Proceedings.
"This is a landmark decision and the best result we could hope for," Robins said in a statement.
"It is disappointing that the abatement can't be reversed, but we are pleased she has won a clear declaration about the Social Security Act 1964 and the law that replaced it, the Social Security Act 2018.
"We hope that the Government will consider an amendment to the Act to remove its discriminatory effect. We are grateful that the Attorney-General was proactive in conceding the case without the need for a hearing."
The Minister for Social Development must now bring the tribunal's declaration to the attention of Parliament and provide a report containing advice on the Government's response to the declaration.
MSD's deputy chief executive of service delivery, Viv Rickard, said the tribunal's finding brought into focus "inconsistencies between the Bill of Rights Act and current law".
"The Ministry, jointly with the plaintiff, Ms Maree Hennessy, filed a memo with the tribunal agreeing a declaration should be issued, avoiding the need to continue with litigation on this issue. We agree with the tribunal's finding that section 71A of the Social Security Act 1964 discriminates on the grounds of employment status," Rickard said in a statement.
"MSD has been following the law as set out in the Social Security Act, and we are obliged to continue to follow the letter of the Social Security Act in the payments we make to those receiving income support.
"For those of our clients who are receiving income support from us and compensation from ACC, we are unable to make any change in practice despite the tribunal's finding.
"The Minister has been advised of the situation and tabled a report in the House on this issue on 20 December 2018. MSD will provide further advice to the Minister as required."