The position of the Church, which has 7.2 million members out of a population of 9.1 million, had been solicited by the government as it prepares a bill on a new "gender neutral" marriage law that it hopes to present to parliament early next year.
"Marriage and (same-sex) partnerships are equivalent forms of unions. Therefore the Church of Sweden's central board says yes to the proposal to join the legislation for marriages and partnerships into a single law," the Church said in a statement.
"According to the Church of Sweden's board the word 'marriage' should however only be used for the relationship between a woman and a man," it said.
Sweden has since 1995 allowed gays and lesbians the right to civil unions, granting them the same legal status as married couples.
But gay and lesbian organisations have long been pushing for the last distinction between heterosexual marriages and homosexual unions to be eliminated.
Sweden's current law from 1987 defines marriage as being between a man and a woman. The government has proposed that the new law strike any reference to gender.
Archbishop Anders Wejryd said in the statement that "there were different opinions on the board, but there was a large majority who felt that the word marriage should only be used for man/woman relationships."
The Church's position in effect rejects the idea of a gender neutral law, since it wants the term "marriage" to apply only to heterosexual unions. But it opens the door for same-sex couples to wed in church.
While heterosexuals can currently marry in either a civil ceremony or a church ceremony in Sweden, homosexuals are only allowed to register their partnerships in a civil ceremony.
If the new legislation is adopted, Sweden, already a pioneer in giving same-sex couples the right to adopt children, would become the first country in the world to allow gays to marry within a major Church.
The Lutheran Church, which was separated from the state in 2000, has since January 2007 offered gays a religious blessing of their union.