The federal lawsuit was filed in Columbia last week by Katherine Bradacs and Tracie Goodwin, who were legally married in Washington, D.C., The State, Columbia, S.C., reported.
South Carolina Gov. Nikki Haley and State Attorney General Alan Wilson are named as defendants in the suit, which challenges South Carolina's Defense of Marriage Law and a 2006 amendment to the state Constitution that bans same-sex marriage.
The law, which was passed by the S.C. House of Representatives by an 82-0 vote in 1996, states that "a marriage between persons of the same sex is void ab initio (from the start) and against the public policy of this state."
The constitutional amendment bars same-sex marriages that are legal in other states from being recognized in South Carolina.
"Although plaintiffs Bradacs and Goodwin were legally married in the District of Columbia on April 6, 2012 ... they are treated as legal strangers in their home state of South Carolina," the lawsuit stated.
"This suit is really about equal treatment of all South Carolina citizens under the law," said attorney John Nichols, who represents the plaintiffs. "We should value people who want to live in a committed relationship, regardless of gender."
Judge Joe Anderson will preside over the case, which will be heard without a jury. No hearing has been set.
Haley and Wilson have not yet commented on the lawsuit.
Interpol investigating stolen passports on missing flight
Senate Democrats to pull all-nighter on climate change