It came just hours after a senior Tory peer called for an independent inquiry into "institutional" Islamophobia in the party.
Baroness Warsi - the first Muslim woman to sit in the Cabinet - warned that the party's failure to address the issue risked damaging Conservative chances at the next election.
According to a report by BuzzFeed, one member of the Facebook group posted: “I am a member and will not be voting for Islam to lead this country."
A Conservative Party spokesperson said: “This Facebook group is in no way affiliated with the Conservative Party and many of the people identified on it are not party members.
“However, we have identified some people who are party members and they have been immediately suspended, pending further investigation.
“When we find evidence of members making offensive or inappropriate comments, we consistently take decisive action. Discrimination or abuse of any kind is wrong and will not be tolerated.”
Lady Warsi 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."
Lady Warsi rejected the claim that the Tories were acting to address the problem.
She told the BBC's World at One programme: "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 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."
Mr Lamb 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 added: "Mr. Lamb was investigated and suspended by his local association back in 2017. He has subsequently resigned from the party.”