The retired neurosurgeon also said Islam, as a religion, was inconsistent with the Constitution. Carson told NBC's "Meet the Press" he believed a president's faith should matter "depending on what that faith is."
"I would not advocate that we put a Muslim in charge of this nation. I absolutely would not agree with that," Carson said. "If it's [a president's faith] inconsistent with the values and principles of America, then of course it should matter."
Fellow GOP presidential candidate Donald Trump came under fire this weekend when he didn't correct an audience member at a campaign event who claimed the president was a Muslim who was not born in the United States. Many presidential candidates -- Democrat and Republican -- criticized him for the incident.
On Saturday, Trump defended himself on Twitter saying that he wasn't "morally obligated to defend the president every time somebody says something bad or controversial about him." He reiterated his defense during his remarks at the GOP Iowa Faith and Freedom Coalition event that night.
He also attended a homecoming at Urbandale High School in Urbandale, Iowa, Saturday night where a student asked him whether he would include a Muslim-American in his cabinet. He said, "Of course ... next question."
Carson, who has been near the top of several presidential polls, said he would consider voting for a Muslim in Congress "[depending] on who that Muslim is and what their policies are."
ABC News has reached out to Carson's campaign for comment.