The public will go to the polls to decide if same sex couples should be allowed to marry on May 22.
Archbishop Eamon Martin said in a letter to parishioners he had "received many letters and messages asking me, as a Bishop, to explain clearly the Church's teaching on marriage".
The leader of the Catholic Church in Ireland said changing the definition of marriage "is not a simple or a trivial matter".
The Archbishop said he could not support a union that would not allow for the procreation of children.
Archbishop Eamon Martin
He quoted a passage from the Catholic Church's recent Extraordinary Synod on the Family in Rome.
"There are absolutely no grounds for considering homosexual unions to be in any way similar or even remotely analogous to God's plan for marriage and family," he said.
His letter continued: "As people of faith, we believe that the union of a man and a woman in marriage, open to the procreation of children, is a gift from God who created us 'male and female'.
"But we are also people of reason, who hold to the truth about human sexuality, grounded in the natural law, that the relationship between a man and a woman is unique.
"How have we got ourselves into the situation that when people stand up to guard the dignity of difference between a man and woman, and speak for the traditional definition of marriage, they are often portrayed as being against freedom, or against equality?
"How is it that many people won't even raise these issues in their families and workplaces for fear of being ridiculed or condemned as homophobic?
"Could we not expect at least some of our legislators to engage in public discussion on both sides of this debate?"
Irish prime minister, Enda Kenny, is supporting a yes vote but has stressed equal marriage would not apply to church or other faith-based unions.
But the Church is up against it with most polls showing 70% of the Catholic country supporting marriage for gay people.
In March a high profile Catholic priest said he would be voting yes.
Fr Iggy O'Donovan said: "It is possible to have deep and passionately-held convictions without seeking to have those convictions imposed by the State on fellow citizens who do not share them.
"Respect for the freedom of others who differ from us is part and parcel of the faith we profess. For these and for other reasons I will be voting Yes".