Support for Flora Scarabello’s campaign has been withdrawn from the party pending an investigation.
It follows an apology from Boris Johnson over the Tories’ response to allegations of Islamophobia in the party.
The Conservatives have come under pressure amid the ongoing row over anti-Semitism in the Labour Party, with the Muslim Council of Britain accusing the Tories of having a “blind spot for this type of racism” and responding with “denial, dismissal and deceit”.
On Wednesday, the Conservative candidate for Luton South, Parvez Akhtar called on Mr Johnson to "unequivocally apologise" for the “hurt and anger” caused by a newspaper column that compared Muslim women to “letter boxes” or “bank robbers”.
The Prime Minister said: "We are going to have an independent inquiry into Islamophobia, anti-Semitism, every manner of prejudice and discrimination, and it will start before Christmas."
Asked if he would apologise for Islamophobia within the Conservative Party, Mr Johnson said: "Of course and for all the hurt and offence that has been caused - of course we do.
"All that is intolerable and it's so important as a country that we don't allow that kind of thing, and that's why we're going to have the independent inquiry."
Ms Scarabello is alleged to have used anti-Muslim language in a recorded telephone conversation, the details of which have not been made public.
A spokesman for the Scottish Conservatives said: “We take allegations like this extremely seriously.
“There is no place in the Scottish Conservatives for anti-Muslim language, or any other form of racial or religious discrimination.
The spokesman said no further comment could be made because a formal complaint had been lodged.
At a hustings event in Perth during the Conservative leadership contest, Ms Scarabello is reported to have asked Mr Johnson whether the Prime Minister needed to be a “loyal husband and father,” in a reference to his extramarital affairs.
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