In a landmark decision issued on Thursday, the supreme court struck down the ruling of a Saint Gallen administrative court last August that recognized the two fathers.
The two men, originally from Saint Gallen in northeastern Switzerland and living in a Swiss registered partnership, had sought to have a California birth certificate recognized by the registry office in their home canton.
The office refused to register the two men as fathers of the child, a decision which the couple successfully appealed to the administrative court, but that court's ruling was appealed by the federal justice department.
The US birth certificate states that the men are the parents of the child.
The child was conceived through artificial insemination of a woman in California who agreed to be a surrogate mother, using the sperm of one of the two partners, the SDA news agency earlier reported.
The supreme court ruled that only the sperm donor can be officially recognized as the father, according to a report from broadcaster RTS.
And it said that the name of the surrogate mother should also be officially registered by the canton of Saint Gallen in its “civil status” register.
To recognize the non-biological father would be the equivalent to authorizing the use of a surrogate mother, which is against the law in Switzerland, the court said, according to the RTS report.
The American birth certificate was based on a California court decision by which the surrogate mother and her husband abandoned their parental responsibilities for the newborn.
The Saint Gallen cantonal department responsible for births and marriages supported the two men but the Swiss federal justice department appealed the canton's decision all the way to the supreme court.
The men expressed their disappointment with the verdict, broadcaster SRF reported.
A lawyer for the pair said the ruling was not in the best interests of the child, the broadcaster said.
The ruling seems to ignore that the lack of genetic relationships are not a bar to parenthood in the case of adoptions.
The couple's last avenue for appeal now lies with the European Court of Human Rights.