The ruling came nearly a week after state Attorney General Dustin McDaniel announced he personally supports gay marriage rights but that he will continue to defend the constitutional ban in court.
McDaniel's office is expected to quickly appeal Piazza's ruling to the Arkansas Supreme Court.
The 2004 constitutional amendment was passed with the overwhelming support of Arkansas voters.
The U.S. Supreme Court last year ruled that a law forbidding the federal government from recognizing same-sex marriages was unconstitutional. Since then, lower-court judges have repeatedly cited the Supreme Court decision when striking down some of the same-sex marriage bans that were enacted after Massachusetts started recognizing gay marriages in 2004.
Since late last year, federal judges have ruled against marriage bans in Michigan, Oklahoma, Utah, Virginia and Texas, and ordered Kentucky, Ohio and Tennessee to recognize same-sex marriages from other states.
In all, according to gay-rights groups, more than 70 lawsuits seeking marriage equality are pending in about 30 states. Democratic attorneys general in several states — including Virginia, Pennsylvania, Nevada, Oregon and Kentucky — have declined to defend same-sex marriage bans.
McDaniel, a Democrat in his final year as attorney general, is the first statewide elected official in Arkansas to support marriage equality. The state's other top Democrats, including Gov. Mike Beebe and U.S. Sen. Mark Pryor, have said they still oppose gay marriage rights.
The plaintiffs argue that their rights to due process and equal protection can't be superseded, even by a state constitutional amendment. Attorneys for the state have argued that an amendment to the state constitution can't itself be deemed unconstitutional.
A group of same-sex couples have also challenged Arkansas' ban in federal court.
Copyright 2014 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.