The country of 4.4 million, which became EU's 28th member in July, has taken steps to improve gay rights, but issues such as same-sex marriage remain highly sensitive in the staunchly Catholic nation.
The referendum was called by the "In the Name of the Family" conservative group after Croatia's centre-left government drafted a law to let gay couples register as "life partners".
The Catholic Church leaders have urged their followers to vote "yes" in the referendum. Nearly 90 percent of Croatians are Roman Catholics.
"Marriage is the only union enabling procreation," Croatian Cardinal Josip Bozanic said in his message to the followers. "This is the key difference between a marriage and other unions."
Croatia's liberal president, Ivo Josipovic, said he voted against amending the constitution. Josipovic said the referendum result must be respected, but added the government is preparing a law to allow some rights to gays and lesbians living together.
"The referendum result must not be the reason for new divisions," Josipovic said. "We have serious economic and social problems. It's not worth it to focus on such issues."
Prime Minister Zoran Milanovic said earlier "this is the last referendum that gives a chance to the majority to strip a minority of its rights".
Conservatives have also started gathering signatures for another referendum, demanding a ban of the Cyrillic alphabet in Croatia. The Cyrillic is used in neighbouring Serbia and by minority Serbs in Croatia. The nationalists blame the Serbs for atrocities committed by their troops during Croatia's 1991-95 war for independence from the Serb-led Yugoslavia.
The EU hasn't officially commented on the referendum, but has clashed with Croatia over some of its other laws, including an extradition law that has prevented its citizens from being handed over to the bloc's other member states, which Croatia had to amend under pressure from Brussels.
Several hundred gay rights supporters marched in the capital, Zagreb, on Saturday urging a "no" vote.
"I will vote against because I think that the referendum is not a festival of democracy, but a festival of oppression against a minority, which fights for its rights and which does not have its rights," Jura Matulic, a university student, said.
- AP