Bevin, the primary opponent of the Senate Minority Leader Mitch McConnell, made the comment Wednesday during a radio interview, Politico said.
"Where do you draw the line?" he asked. "A person may want to define themselves as being married to one of their children so that they can then in fact pass on certain things to that child, financially and otherwise."
Bevin spokesman Rachel Semmel said Thursday that the candidate does not see a comparison between gay marriage and incest.
"He was discussing the implications of the legal rights related to this issue such as hospital visitations and benefits. To imply otherwise is ridiculous," Semmel said.
During the interview, Bevin said that marriage should be up to states, but added that he if is elected to the Senate, he will support defining marriage as between a man and a woman.