In 2006, Virginians voted to add wording to the state constitution that defines marriage as between a man and a woman.
The law prevents Virginia from recognizing same-sex marriages that may be recognized in other states.
A team of ACLU lawyers will argue the Virginia law is unconstitutional because it violates the U.S. Constitution's guarantee of equal protection under the law.
"Thousands of Virginia couples are already living the deep commitment associated with marriage, without legal recognition of their relationships. They and their children deserve the legal protections that come with state-recognized marriage," ACLU of Virginia Executive Director Claire G. Gastañaga said in a statement.
"There is no rational reason for denying these loving couples the freedom to marry and every reason to grant them the same recognition by civil authorities that opposite-sex couples have," she added.
CBS 6 has reached out to the Virginia Attorney General's office for comment.
"We haven’t yet seen the official filing and had an opportunity to review it," Attorney General's office spokesman Brian Gottstein said in an email.
Similar suits are being filed in West Virginia and Pennsylvania.