Speaking to MSNBC's Chuck Todd on Sunday's Meet the Press, Carson said that he would only support a candidate for president whose faith was "consistent with the values and principles of this country."
He then clarified the remark, saying he believed Islam does not pass that particular test.
Carson went on to say he would be in favor of voting for a Muslim to serve in Congress, but only if their faith was "consistent with things that would elevate this nation for everybody to succeed and bring peace and harmony."
Current GOP front-runner Donald Trump has found himself in the middle of a growing controversy after he failed to correct a man at a rally who said, "We have problem in this country. It's called Muslims. We know our current president is one. You know he's not even an American. We have training camps in this country where they want to kill us. When can we get rid of them?"
Historian Kevin M. Kruse noted that the only major part of the U.S. Constitution where religion is directly referenced is a passage explicitly saying "no religious test shall ever be required as a qualification to any office or public trust under the United States."
Carson is currently polling second in the race for the Republican presidential nomination at 18.8% support, according to the poll averages kept by Real Clear Politics.
In 2008, Republican and former Secretary of State Colin Powell denounced racism in the GOP, saying that the "really right answer" to questions about whether President Obama is a Muslim was "What if he is? Is there something wrong with being a Muslim in this country? The answer's no, that's not America. Is there something wrong with some 7-year-old Muslim-American kid believing that he or she could be president?"
According to Carson, the answer is yes.
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