Gay couples can be wed in only some parts of Alabama after the state's chief justice issued an order to stop judges from granting licences.
The Supreme Court has refused Alabama's request to stop the marriages.
But some counties have followed the order of Chief Justice Roy Moore and will not grant marriage licences to same-sex couples.
Judges in other parts of in the conservative state have stopped conducting weddings altogether.
In one of the counties refusing to hold marriages, Autauga County, a female minister was arrested after offering to perform a same-sex marriage at the judge's office.
Anne Diprizio was charged with disorderly conduct after refusing to leave when asked, the Montgomery Advertiser reports.
Many same-sex couples living in the affected counties travelled to major cities such as Montgomery and Birmingham to get marriage licences.
But at least six gay couples, who had hoped to marry, filed federal lawsuits after Mobile County's marriage licence division did not open on Monday.
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