A bill to put the amendment question on the ballot won state Senate approval Tuesday by a 30-16 margin, a day after the state House passed it 76-41, CNN reported.
Same-sex marriage already is illegal in North Carolina, but supporters of the amendment say the ban should be made part of its state Constitution.
Opponents call the amendment unnecessary and say it discriminates against gays and lesbians.
"We think the people of this state -- not judges, bureaucrats, or politicians -- should define marriage, which I personally believe should be between one man and one woman," Senate President Pro Tem Phil Berger, a Republican, said in a statement after the Senate vote. "We look forward to eight months of healthy debate before voters decide this issue at the polls."
Democrats had blocked a constitutional ban on same-sex marriage for years but Republicans now control the Legislature.
Sen. Josh Stein, a Democrat, said: "Most of us have gay neighbors, co-workers, friends and family members. Know that if you vote for this amendment, you will cause them pain."
Gov. Bev Perdue, echoing some lawmakers, argued the Legislature should focus on more pressing issues like the economy and creating jobs.
"I'm focused on solving problems and creating jobs," the governor said. "This partisan exercise does neither: Same-sex marriage is already illegal in North Carolina, and this constitutional amendment would not create a single job."
Like some opponents, Perdue said, the amendment could actually hurt the state's ability to attract new businesses.
Attkisson leaves CBS News, reportedly over network's 'liberal bias'
Duggar sisters unveil Christian dating rules in new book