Lars Gårdfeldt and Lars Arnell, who are both priests in the Church of Sweden, alleged discrimination when their marriage was classified as a civil partnership.
The couple have lost their case in the district court, the court of appeal and now in the Supreme Administrative Court, Sweden's highest court.
The couple argued that a same-sex marriage entered into in accordance with Canadian law should be recognized in Sweden, despite the fact that there is no legal basis for it under current Swedish law.
In their application to the court the couple argued that the "tax authorities can make an exception for a marriage where one party is under-age but not for homosexuals."
The authority confirmed that it does make exceptions to Swedish law with regard to under-age couples legally married overseas. But only for marriages involving a man and a woman.
Gårdfeldt, a prominent commentator on homosexual issues both within and outside of the church, reacted to the ruling, calling it discriminatory.
The court referred to the definition contained within Swedish legislation covering marriage, concluding that the term applies only to a union between a man and a woman while a union between two people of the same sex is designated as a partnership.
The court concluded in its judgement that even if this union in a foreign state is classified as marriage it is, according to current Swedish law, classified as a partnership.