The BBC reported that more than 85,000 fixed penalty notices, which can be as high as £10,000, have been issued in England since the pandemic began, and 8,000 in Wales. The JCHR report noted that coronavirus rules have changed at least 65 times since March 2020.
MPs on the Joint Committee on Human Rights said the system is "muddled, discriminatory and unfair".
The JCHR, which is made up of MPs and peers, said it had "significant concerns" about the validity of fines, the inadequacy of the review and appeal process, the size of the penalties and the criminalisation of those who could not afford to pay.
"The whole process disproportionately hits the less well-off and criminalises the poor over the better off," said committee chairwoman Harriet Harman.
While the committee recognised swift action had been needed in the face of the pandemic, the government needed to ensure rules were clear, enforcement was fair and that mistakes could be rectified, she said, adding: "None of that is the case in respect of Covid-19 fixed penalty notices."
Ms Harman said police had a difficult job enforcing the rules during the pandemic, but warned a "lack of legal clarity" meant there could be a large number of wrongly issued fines.
A government spokesperson said it was right there were consequences for those who most flagrantly breached the rules.