Their outspoken statement came after Roseanna Cunningham told the Scottish Parliament that an earlu review of the controversial laws, which are intended to stamp out religious sectarian abuse at football matches, would be nonsensical.
In a statement on their website, Celtic said: "The Scottish Government introduced the legislation in 2012 and promised a review after two full football seasons of operation. However, Celtic believe that 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 which is consistent with the club´s proud history and reputation.
"We believe the Scottish Government should review, as a matter of urgency, the way in which this unhelpful and counter-productive Act is operating.
"Celtic have always valued a positive relationship with the police and we are concerned that they too have now been put in the position of enforcing legislation which is provocative and does not command widespread respect.
"The Scottish Government has conceded the need to review the workings of the legislation but we see no need for delay since there is plenty of evidence available, not least from the comments of Sheriffs who have had to deal with cases arising from it.
"It would be helpful if the new season could kick off in August with these issues resolved so that everyone could concentrate on promoting the best possible environment for Scottish football and marginalising unwelcome influences which attach themselves to it."
Earlier today Cunningham rejected suggestions that the timetable for reviewing the laws should be brought forward from the deadline, due in August 2015, when Stirling University researchers are due to publish findings.
The Offensive Behaviour at Football and Threatening Communications (Scotland) Act received Royal Assent in January 2012.
An agreement was made at the time 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.
Ms Cunningham told MSPs on Holyrood's Justice Committee: "Until August 2014, they haven't got all the information. It's at that point they start to be doing all the analysis of the two full years work. We are now a good two years down the line from this being implemented and we're coming close to the end of that two-year review period the Act provided for.
"I just don't really see any great need for that to be changed. I couldn't now step in and ask them to do something differently to what they've been instructed.
"That process, because it's being done independently, because it's being done through Stirling University, is going to give a proper, comprehensive, quality-assured, evidence-based evaluation which 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, she replied: "No, it would be nonsensical to do something while this review was ongoing when we know the review is going to be published - they're the independent researchers, they're the ones that will be able to tell us something needs to be tweaked or not."
The legislation gives police and prosecutors new powers to tackle sectarian songs and abuse at and around football matches, as well as threats posted on the internet or through the mail. It created two distinct offences, punishable through a range of penalties up to a maximum five years in prison and an unlimited fine.
Some football fans say the legislation created problems for ordinary supporters.
An advisory group set up by the Scottish Government reported in December that sectarianism remains a significant force in society.
But the problem has "had its day" with a large groundswell of people tired of "worn-out rhetoric", the independent group concluded.