The prime minister should "unequivocally apologise for his comments about Muslim women", a Tory parliamentary candidate has said.
Parvez Akhtar said there was "blatant discrimination" in the party toward individuals and in the policy agenda.
This comes as the Muslim Council of Britain accused the Tories of failing to tackle Islamophobia in the party.
Government minister Robert Jenrick insisted his party had "no tolerance whatsoever of racism".
But in a statement Mr Akhtar, the candidate for Luton South, said he had personally experienced two occasions of "anti-Muslim hatred within the party".
Although he said he believed that "a Conservative government is the best thing for our country including for Muslim communities" he went on to say a newspaper column by Boris Johnson's about Muslim women had caused "hurt and anger" in the Muslim community.
Writing in the Telegraph last year, Mr Johnson said that Muslim women wearing burkas "look like letter boxes". During a BBC Question Time programme, Mr Johnson said he regretted any offence he had caused in articles about race during his journalistic career.
Mr Akhtar said the effect of the column has been "to reinforce the widely held view that the Conservative Party has a blind spot when it comes to Muslims".
He said it was a difficult issue to raise but added he could "no longer remain silent as I would be complicit in the blatant discrimination which exists not only within the party towards individuals but also when it comes to the policy agenda".
He called on Mr Johnson to apologise for his previous comments and to agree to hold a "a full independent and transparent enquiry" into Islamophobia in the Conservative Party.
Earlier, the Muslim Council of Britain - an umbrella organisation of various UK Muslim bodies - released a report setting out a series of policies and pledges designed to tackle Islamophobia it wants political parties to adopt.
The group says all parties should investigate instances of Islamophobia within their ranks and ensure they have disciplinary procedures in place to tackle it.
Muslims are underrepresented in politics and other areas of public life, it says, and calls on all political parties to take concrete steps to encourage Muslims to join and to seek election.
On Tuesday the group said it was "abundantly clear to many Muslims that the Conservative Party tolerates Islamophobia" and "allows it to fester in society".
The group has previously said the Conservative's unsuccessful London mayoral campaign against Sadiq Khan was an example of "tolerance for Islamophobia" within the party.
Speaking on the BBC's Today programme on Wednesday, Communities Secretary Robert Jenrick insisted the Conservatives had "no tolerance whatsoever of racism, prejudice, or discrimination of any kind".
"I want to see by the end of this year, as the prime minster has promised, a thorough review of prejudice, racism and discrimination within the party," he said.
The review would be led by independent individuals, he said, and the findings made public.
The Conservative Party has so far declined to say when the terms of reference for an inquiry would be published.
During the Conservative leadership contest debate in June, Sajid Javid, the then home secretary, asked his fellow candidates if they would support an independent inquiry into allegations of Islamophobia in the party and they backed one.
In August, party chairman James Cleverly said there would be an inquiry. But in November the Prime Minister Mr Johnson appeared to rule out a specific review into Islamophobia saying the party would hold "a general investigation into prejudice".
Meanwhile Labour has been criticised by Chief Rabbi Ephraim Mirvis who said "the overwhelming majority of British Jews are gripped by anxiety" at the prospect of a Labour victory in 12 December's general election.
"A new poison - sanctioned from the very top - has taken root" in the party," he said.
Labour leader Jeremy Corbyn insisted his government would protect "every community against the abuse they receive".
The names of the other prospective parliamentary candidates standing in Luton South can be found here.