The club called for an immediate review of the "unhelpful and counter-productive" Offensive Behaviour At Football And Threatening Communications Act, but Communities Safety Minister Roseanna Cunningham said it would be "nonsensical" for an early assessment to be carried out.
The Act, which received Royal Assent in January 2012, gives police and prosecutors powers to tackle sectarian songs and abuse at and around football matches, as well as threats posted on the internet or through the mail.
An agreement was made at the time the laws came into force for the Scottish Government to review the operation of the offences after two full football seasons and to report back to Parliament one year later. But concerns have since been raised by fans about police tactics and the Act in general.
Celtic Football Club called for a review of the Act's impact to be brought forward "as a matter of urgency". A statement from the club added: "Celtic believe there is already sufficient evidence of the Act's 'unhelpfulness and negative impacts' to justify an immediate review with action to follow.
"Celtic have all along opposed this legislation, which has been used to create a general presumption that different laws should apply to football supporters as distinct from society as a whole.
"This has inevitably led to a sense of discrimination across Scottish football and has brought the law into disrepute when tested in the criminal courts. It has also acted as a barrier to our own efforts to encourage supporters to behave in a way consistent with the club's proud history and reputation."
The introduction of the legislation prompted a rally and protest involving thousands of football fans in Glasgow over what they claimed were "disproportionate" measures to crack down on hate crime.
Fans Against Criminalisation - which describes itself as "an independent umbrella group comprising the Green Brigade, Celtic Trust, Celtic Supporters' Association, Affiliation of Registered Celtic Supporters' Clubs and Association Of Irish Celtic Supporters' Clubs" - claimed the Act led to "heavy-handed" policing.
But Ms Cunningham yesterday rejected suggestions to look at the legislation ahead of a previously agreed August 2015 deadline, when Stirling University researchers are due to publish findings.
She told the Scottish Parliament Justice Committee the academics conducting the review would not have all the information they needed until August this year.
She added: "I do not really see any great need for that to be changed. I could not now step in and ask them to do something differently to what they have been instructed."
"That process, because it is being done independently, is going to give a proper, comprehensive, quality-assured, evidence-based evaluation that will be - I hesitate to say incontrovertible, because nothing is ever incontrovertible - but it will be as solid a piece of work as you could possibly expect."
Asked if anything could happen before the 2015 deadline, such as in interim report, Ms Cunningham replied: "No, it would be nonsensical to do something while this review was continuing when we know the review is going to be published; they are the independent researchers, they are the ones that will be able to tell us something needs to be tweaked or not."
Labour MSP Graeme Pearson, who has led the calls for a review, said: "From the outset it has been apparent this legislation has caused more trouble than it was aimed to resolve. It is always difficult for a Government to admit it got it wrong and this Government particularly."