Christian legal group ADF International has filed an expert brief with the European Court of Human Rights in support of the man known as A.A. (anonymised for security reasons).
ADF said if he is sent back to his home country he could face severe social and formal persecution, with punishments ranging from lengthy imprisonment to death.
"International law is very clear on the fact that no country should return a refugee to territories where his or her life could be in danger," said Jennifer Lea, Legal Counsel with ADF International.
"Afghanistan is not a safe place for a Christian convert.
"The Court should ask Switzerland to stop turning a blind eye to the situation of religious minorities in Afghanistan."
While the Afghan Constitution protects religious freedom in general, it also defines Islam as the state religion and prohibits the enactment of any law contradicting Islamic beliefs.
ADF added that Afghanistan's civil courts investigate "crimes against God."
Also, crimes like apostasy, blasphemy, anti-Islamic writings or speech, and proselytising are considered serious and punishable by beheadings for males, confiscation of property, and inheritance limitations.
ADF has urged Switzerland to defend religious freedom.
Robert Clarke, director of European advocacy for ADF International, said: "The case of A.A. v. Switzerland provides the Court with the opportunity to remind its 47 Member States that they each are legally required to defend religious freedom.
"This means much more than demanding a convert practice his faith in secret.
"Sending a refugee back to a country where they face persecution because of their faith is incompatible with the Convention."
Afghanistan is number two on Open Doors' 2018 World Watch List which ranks 50 countries where Christians face the most extreme persecution.
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