Andrew Malkinson spent 17 years in prison for a crime he did not commit
The justice secretary said he was considering backdating new rules which mean wrongly convicted people will no longer have prison living costs deducted from compensation.
Alex Chalk said he was looking into three cases “very carefully” after the rule was scrapped.
It comes after Andrew Malkinson, who spent 17 years in jail for a rape he did not commit, was cleared.
Mr Chalk said his “blood ran cold” when he heard about what had happened.
“It’s appalling to think of an injustice in that way,” he told BBC Breakfast.
People who are wrongly jailed for more than 10 years can be paid up to £1m under a government compensation scheme.
Under previous rules, savings made on living costs such as food and housing while in prison could be deducted from compensation.
This rule was scrapped on Sunday, however, the government has not committed to reimbursing wrongly convicted people who have previously had the deduction applied to their compensation.
Mr Chalk said he was looking at three previous cases “very carefully”
“Certainly since 2006, there have been three cases where deductions have been made and none in the last 10 years. I am looking at it,” said Mr Chalk.
“Although of those three cases, the reductions from their compensation reward have been 3%, 3% and 6% so it’s important to get some perspective.
“There is also issues in the public interest about retrospectivity – there is normally a rule that you shouldn’t make rules retrospective – but I’m considering this all in the round.”
Mr Malkinson, who has always maintained his innocence, was jailed in 2004 for an attack on a woman in Salford, Greater Manchester.
The prosecution case against him was based only on identification evidence.
He was cleared last month after new DNA evidence linking another suspect to the crime emerged.
Court of Appeal judges have since called the original conviction “unsafe” because Greater Manchester Police did not disclose images during his trial.
Mr Chalk also said he would be willing to meet Mr Malkinson “in principle” to discuss the case.
But he added: “There has been some talk of potential litigation so of course – as is normal – you have to consider whether you can meet in the context of litigation.”
“If it went wrong, as appears in this case, then we absolutely have to get to the bottom of who got it wrong,” he added.
Why not follow BBC North West on Facebook, Twitter and Instagram? You can also send story ideas to northwest.newsonline@bbc.co.uk
