The lawsuit was filed Monday in federal district court in Nashville. It argues that Tennessee's laws violate the federal Constitution's guarantees of equal protection and due process.
Under a U.S. Supreme Court ruling, gay couples who are legally married in states that allow it are given equal federal footing with all other married Americans.
In Tennessee, however, marriage between partners of the same gender is prohibited by state law and constitutional amendment.
The filing Monday comes amid New Jersey Gov. Chris Christie's decision to drop his legal challenge to same-sex marriage, making New Jersey the 14th state to allow gay marriages.