Activist Gareth Lee took Ashers Baking Company to court with the support of Northern Ireland's Equality Commission after the order was turned down.
District Judge Isobel Brownlie said: "The defendants have unlawfully discriminated against the plaintiff on grounds of sexual discrimination.
"This is direct discrimination for which there can be no justification."
The bakery has been ordered to pay £500 in damages but it can appeal.
General Manager Daniel McArthur said: "We're extremely disappointed with the judgment.
"The ruling suggests that all business owners will have to be willing to promote any cause or campaign no matter how much they disagree with it. Or as the Equality Commission has suggested, they should perhaps just close down, and that can't be right.
"But we won't be closing down, we certainly don't think we've done anything wrong and we will be taking legal advice to consider our options for appeal."
She accepted the McArthur family had "genuine and deeply held religious beliefs" but said this was not a reason to decline the sale.
The case was brought by the Equality Commission of Northern Ireland after Mr Lee tried to order a cake featuring Sesame Street puppets Bert and Ernie with the slogan Support Gay Marriage.
The bakery had said they were unaware of Mr Lee's sexuality and they declined the order because they could not bake the cake which supported same sex marriage.
Judge Brownlie disagreed with the bakery: "They must have known or had the perception that the plaintiff was gay.
"They must have known that the plaintiff supported gay marriage or associated with others who supported gay marriage."
Mr Lee told the court he felt like a lesser person when his order was rejected.
"[Ashers] are in a business supplying services to all. The law requires them to do just that," the judge added.
The judge said the Christian bakery had treated Mr Lee "less favourably" because of his sexuality and this was contrary to the law.
She said she had "no doubt" that a cake supporting traditional marriage would have been provided, "it is the word gay that the defendants took exception to," she added.
"They were contracted on a commercial basis to bake and ice a cake.
"The plaintiff was not seeking support or endorsement."
Daniel McArthur, his wife Amy & two children
Speaking before the verdict manager Mr McArthur said: "We depend fully on God, and God gives us our husbands and our wives in these difficult times to help us through them.
"There's been many parts of the Bible which I've read which have been of great encouragement, but particularly Psalm 22.
"When I'm reading it I'm thinking about what Jesus has been through, and what He's been through for me and for our family, and I know that if He's been through that, God in turn will give us the strength to deal with the trials which we have to go through."