With 97 percent of the vote reported, 395,468, or 71 percent, voted "yes," and 163,766, or 29 percent, voted "no."
Meanwhile,was prepared to vote Wednesday on a bill that would allow same-sex couples to enter into civil unions. The bill has broad support in both Democratic-controlled chambers of the Legislature.
Gay marriage is already banned under Kansas law, and the law is not being challenged. But supporters of the ballot measure said the ban must be in the Kansas Constitution to insulate it from legal challenge.
Most voters appeared to brush aside critics' arguments that the amendment could have unexpected consequences, such as preventing companies from offering health benefits to employees' partners, gay or heterosexual.
"The way marriage is in the Bible, God says it's between man and woman," said Sharon Kent, 58, of the Kansas City suburb of Mission. "I don't have a problem with gays being together, living together, but I have a problem with them getting married."
Matt Foreman, executive director of the National Gay and Lesbian Task Force, said the vote was not surprising, given results in other states.
"What is appalling is the continued silence and inaction of people of faith and people of goodwill to speak out, to stand up to this wave of attacks against gay people," he said.
The Rev. Terry Fox, senior pastor at Wichita's Immanuel Baptist Church and a leader of the campaign for the proposal, said he expects opponents to challenge the amendment in court, though he is confident it will stand up.
"We always felt like if Kansans were given an opportunity to vote, they would vote strongly to protect marriage and defend marriage in the way it has traditionally been defined," Fox said. "The real winner here was marriage itself."
Republican state Attorney General Phill Kline had said the amendment was "an unfortunate, necessary reaction to activist courts."
Among the opponents was Democratic Gov. Kathleen Sebelius, who said she supported the existing state law and viewed it as sufficient.
"I don't think we need a constitutional amendment, and particularly a constitutional amendment that goes far beyond the bounds of that law," she said.
Kansas becomes the 18th state with such a prohibition in its constitution. Alabama, South Dakota and Tennessee plan elections next year on constitutional bans, and proposals are pending in 13 other states, according to the National Conference of State Legislatures.
Vermont is the only state that recognizes civil unions, while Massachusetts allows same-sex couples to marry.