The Joint Committee on Human Rights (JCHR) called the penalties “muddled, discriminatory and unfair”.
Fines of up to £10,000 could be given for breaches of the rules - regardless of a person's financial circumstances.
There has been confusion between government advice, guidance and the law, too, the committee claimed.
Covid-19 guidance had changed at least 65 times since March 2020, providing “obvious challenges for police”, according to the report.
Meanwhile the law had not changed very much.
Committee chairman Harriet Harman said: “Our inquiry has demonstrated that coronavirus regulations are neither straightforward nor easily understood either by those who have to obey them or the police who have to enforce them.
“With fixed penalties of up to £10,000 awarded irrespective of the individual’s financial circumstances, there is much at stake."
Ms Harman said there was an "unfair system" with "clear evidence that young people, those from certain ethnic minority backgrounds, men, and the most socially deprived, are most at risk".
She said: “Those who can’t afford to pay face a criminal record along with all the resulting consequences for their future development.
“The whole process disproportionately hits the less well-off and criminalises the poor over the better off.”
More than 85,000 fixed penalty notices have been issued since March last year.
A Crown Prosecution Service (CPS) review of prosecutions brought under coronavirus regulations that reached open court found in February 2021 that 27% were incorrectly charged.
The committee's report raised "significant concerns" about the validity of the fines, the inadequacy of the review and appeal process, and the size of the penalties.
The report read: “It is astonishing that the Coronavirus Act is still being misunderstood and wrongly applied by police to such an extent that every single criminal charge brought under the Act has been brought incorrectly.
“While the coronavirus regulations have changed frequently, the Act has not, and there is no reason for such mistakes to continue.”
“It is possible to tell from penalties that have not been paid and have then progressed through the system towards a prosecution, that a significant number of FPNs are incorrectly issued,” the committee added.
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Committee chairman Ms Harman said: “Swift action to make restrictions effective is essential in the face of this terrible virus.
“But the government needs to ensure that rules are clear, enforcement is fair and that mistakes in the system can be rectified.
“None of that is the case in respect of Covid-19 fixed penalty notices.”
She acknowledged the “difficult job” police had in enforcing the lockdowns, but said there could be a large number of wrongly issued fines because of a “lack of legal clarity”.