Leading a new report to be unveiled in Westminster Cathedral on Monday, Dominic Grieve also suggested the government's anti-extremism programme Prevent is not always trusted among Muslims.
In 'The Missing Muslims: Unlocking British Muslim Potential for the Benefit of All', the Conservative MP recommends a review of the scheme.
Mr Grieve and his fellow commissioners behind the report suggest tackling extremism and radicalisation would be "better achieved with a programme that has greater trust, particularly from the UK's Muslim communities".
Speaking with Premier about the commission behind the report, he said: "It was based on going around the country and taking evidence from Muslims and non-Muslims as well... about... what worked and also what the obstacles were to wider participation."
The document also warns that a fear of discrimination is deterring young British Muslims from engaging in aspects of public life such as politics. It also reports a strong sense that Muslims and Islam and "unfairly targeted".
They also call upon the government to adopt a definition of anti-Muslim prejudice, similarly to how it adopted a definition of anti-Semitism last year.
The report cites "significant scepticism across British society" about the integration of Muslims and warns of the risk of a "downward spiral of mutual suspicion and incomprehension".
The commissioners also urged the Independent Press Standards Organisation to consider reporting guidelines for the media when covering Muslim issues.
A Government spokeswoman said: "We're clear there should be no conflict between being British and being Muslim, and that active participation in public life should be open to all.
"We've invested over £70 million on the integration programme since 2010. The findings of this report will help us take forward our work in creating a society where everyone - of any faith, ethnicity or background - feels valued and can participate fully."