Former minister Baroness Warsi warned that the party's failure to address the issue within its ranks risked damaging Conservative chances at the next election.
Dewsbury-born Lady Warsi, who was the first Muslim woman to have a seat at the Cabinet table, said there was a "deep-rooted problem" in the party and Theresa May had failed to act.
Her intervention came after Tory council candidate Peter Lamb quit after coming under fire for social media comments about Islam.
Mr Lamb was due to stand in Harlow, Essex, in May's local elections despite having been disciplined in 2017.
In 2015, he tweeted: "Islam like alcoholism [sic]. The first step to recovery is admit you have a problem."
Later in the same year, he tweeted: "Turkey buys oil from ISIS. Muslims sticking together."
He said: "I deeply regret my remarks on social media. At no point did I intend to cause any offence to the Muslim community. I have reflected on my comments and decided that I should step down as a local election candidate and resign (from) the Conservative party with immediate effect."
A Conservative spokesman said: "Mr. Lamb was investigated and suspended by his local association back in 2017. He has subsequently resigned from the party.
"Discrimination or abuse of any kind is wrong and will not be tolerated.
"When CCHQ have been made aware of cases we have acted swiftly and decisively, suspending or expelling those involved and launching an immediate investigation under our party's code of conduct."
University of Leeds-educated Lady Warsi rejected the claim that the Tories were acting to address the problem.
She told BBC Radio 4's World at One: "We have a deep-rooted problem of anti-Muslim comments, Islamophobic comments, racist comments that have been made right from the top - from MPs through to councillors, council candidates, members, linked groups."
She said she had previously suggested an internal inquiry to deal with the issue, but added: "I think it has now gone beyond that and we need an independent inquiry."
She went on: "We cannot have a situation where a mainstream political party is sending out a message in the way it is acting that certain parts of our country, certain communities in our country, certain citizens in our country, are simply not welcome in our party and therefore are creating this environment in which, sadly, I think we will feel the impact at the next election."
Lady Warsi urged Tory chief executive and treasurer Sir Mick Davis to act, claiming Mrs May and party chairman Brandon Lewis "have failed".