"No serious, objective, critical review can be undertaken by someone with such a track record – rather we should expect him to promote a hardening of policies towards Muslims," the statement read.
"So, if Muslim organisations engage with this review, it strengthens its legitimacy and its power to recommend policies more harmful to the community."
Organisations lined up to join the boycott include the Federation of Student Islamic Societies, the Islamic Human Rights Commission, and the Muslim Lawyers Action Group.
Shawcross headed the Charity Commission for England and Wales between 2012 and 2018, at a time when the watchdog was strongly accused by rights groups of anti-Muslim bias.
As a director of the neo-conservative Henry Jackson Society think tank in 2012, Shawcross appeared to indicate his belief that a clash of civilisations was brewing between Europe and its Muslim citizens.
"Europe and Islam is one of the greatest, most terrifying problems of our future. I think all European countries have vastly, very quickly growing Islamic populations," Shawcross said in a video filmed at the time.
Shawcross has also been slammed for his views on torture, having previously described waterboarding as an "enhanced interrogation technique" that would "very likely" produce valuable information.
Speaking to The Guardian, Shawcross said his views have been "misrepresented" and that he "attempted to deal head-on with the thorny moral and legal issues that emerged as the west responded to the threat of Islamist terrorism after 9/11".
The UK government first announced its review of Prevent in January 2019 amid long-standing criticism from activists. Under the strategy, schools, NHS trusts, local authorities and prisons have a statutory duty to report concerns about individuals perceived to be at risk of radicalisation.
Recent figures show that just 11 percent of Prevent referrals were deemed to be legitimate radicalisation risks.
In its statement on Wednesday, the coalition of boycotting groups said the Prevent strategy's "harms include profiling and targeting Muslim children (even as young as four), making the Muslim community 'a suspect community', demonising aspects of Islam, and silencing legitimate speech".
Shawcross insisted in a letter to Prevent practitioners last month that he will be "open minded" and that the review will "look at the effectiveness of present strategies to protect vulnerable people from being drawn into terrorism and make recommendations for the future".
Critics of Prevent and the review, however, say that a truly independent assessment of the counter-radicalisation strategy would go perhaps as far as considering scrapping the programme altogether.