Rowan County clerk Kim Davis has been summoned to the hearing before US District Judge David Bunning.
She has refused on several occasions to allow the wedding of two men to go ahead because, she says, it goes against her Christian faith.
Asked on who's authority she declined to give the licenses she replied "God's authority".
Ms Davis' deputy clerks have also been ordered to appear. Judge Bunning could hold Ms Davis in contempt, which can carry hefty fines or jail time.
She stopped issuing licences to all couples in June after the US Supreme Court legalised gay marriage.
The couples who originally sued in the case have asked Judge Bunning to punish Ms Davis with fines, but not jail time.