Carrie Prejean is Miss California , runner up at Miss USA, claims that she lost her crown because he opposed gay marriages.
“We live in a land where you can choose same-sex marriage or opposite marriage,” said Ms Prejean, in a section of the show that has become a popular clip on YouTube.
“I believe that a marriage should be between a man and a woman,” she continued.
“No offence to anybody out there, but that’s how I was raised.”
The remarks drew a mixture of booing and applause from the audience.
Speaking after the show, which was broadcast on Sunday evening in the US, Ms Prejean said: “I wouldn’t have had it any other way. I said what I feel. I stated an opinion that was true to myself and that’s all I can do.”
Hilton said he had been “floored” by Ms Prejean’s answer, which, he said, “alienated millions of gay and lesbian Americans, their families and their supporters”.
He told ABC News: “She lost it because of that question. She was definitely the front-runner before that.”
Keith Lewis, who runs the Miss California competition, released a statement condemning Ms Prejean’s comments.
“As co-director of the Miss California USA, I am personally saddened and hurt that Miss California believes marriage rights belong only to a man and a woman.”
The issue of same-sex marriage is a flashpoint in American politics.
Four US states now allow gay marriage, but many other states have passed legislation outlawing it.