Hammond opposes Prime Minister David Cameron's plan to legalize marriage for same-sex couples. Pink News reported Friday he made the comment to the University of London students.
Joe Rayment, one of the students, told The Guardian Hammond did not use the word "incest."
"When I asked Philip Hammond what right the state has to tell two people in love that they can't get married, he said: 'Well, siblings can't get married either.' We found this a very offensive and quite disgusting thing for him to say," Rayment said.
Hammond was at the campus in Surrey for a talk to politics students. Rayment said he and a friend, Jack Saffery-Rowe, 19, who is gay, talked to Hammond while asking him to meet with protesters outside.
"Philip Hammond was very slippery in the meeting," Rayment said. "We were unraveling his arguments and picking them apart and he avoided any of our arguments."
Cameron's Conservative Party is split on the issue of gay marriage and its members of Parliament are being allowed to vote their consciences on the issue. It is expected to pass with support from Labor and Liberal Democrat MPs.