The defence secretary and Conservative MP was accused making the comments during a meeting with students on Friday.
Joe Rayment, chairman of the Royal Holloway Students’ Union who was present during the talk, said Hammond's remarks came when confronted about his opposition to same-sex marriage.
He said: "I asked him what right the state has to tell two people who are in love that they can’t get married. He said: 'Well, we don’t allow siblings to get married either.'
"We said something along the lines of the fact that homosexuality is nothing like incest. But he skirted over it and he did not apologise for using that comparison."
Also present at the meeting was the union representative for the university's gay community, Jack Saffery-Rowe.
Writing on a blog that night, Saffery-Rowe said: "When questioned why I shouldn’t have the same rights as a heterosexual couple, he brushed the question aside as a ‘silly game’ talking about human rights.
"And when asked why the state should be allowed to say who can and who cannot have their relationship recognised by the law, he retorted that you wouldn’t allow ‘two siblings who loved each other to get married’.
"He equated the love of a same-sex couple with incest..."
A spokesman for Hammond told The Guardian: "It's untrue. He didn't equate equal marriage to incest."
Hammond is alleged to have made the comparison ahead of a Commons vote on same-sex marriage next week, an issue he has previously described as "too controversial".
Students at the University of London Royal Holloway’s Egham campus in Surrey had planned to lobby the minister after he made clear he is against David Cameron's plans to allow gay couples to marry.
According to Pink News, Hammond, who was at the university to talk about British security, was confronted by around 70 students waving pro-gay marriage placards.