The Free Church of Scotland said this would offer greater protection to celebrants who did not want to carry out marriage ceremonies for gay couples.
A conscience clause could also help protect teachers who do not want to teach pupils about same-sex marriage as part of their classes, the Free Church said.
Medical staff who are opposed to abortion can refuse to play any part in the procedure if it goes against their beliefs, with the conscience clause allowing them to take this stance.
A Free Church spokesman said: "The legislation has worked well for abortion, another deeply contentious moral issue, and it would make sense to have similar provision for same-sex marriage."
In June the Scottish Government published legislation that, if passed by Holyrood, will allow same-sex couples to get wed.
Under the SNP administration's plans, religious bodies would have to opt in to perform same-sex marriage ceremonies.
If a religious group does decide to do this, protection will also be offered to individual celebrants who feel it would go against their faith to carry out gay weddings.
But the Free Church of Scotland, which is opposed to same-sex marriage, claimed there was a "lack of clarity from the Scottish Government on how this legislation will affect individuals who believe marriage is only between a man and a woman". The spokesman added: "We suggest the legislation is amended and adopts a conscientious objection clause similar to that of the 1967 Abortion Act with regards to the celebration of same-sex marriages.
"This would provide indisputable guidance which would be hugely helpful, rather than having to establish precedents through the courts."
The Free Church wants "some reassurance that in the eyes of the state it will still be legal to believe that marriage is between a man and a woman, that those who hold to this traditional view will not be subject to prosecution and that they will be free to express their opinions", the spokesman said.
It said: "Given what has already happened in England - where a court case is being brought against the Church of England with the ink barely dry on the Royal Assent - there is no doubt that we will see similar instances north of the Border. The issue is simply not going away"
As well as publishing the Marriage and Civil Partnership (Scotland) Bill, the Scottish Government published details of an agreement with the UK Government on changes to be made to the Equality Act to protect individual celebrants who may not want to conduct same-sex ceremonies even if their church, as an organisation, backs them.
Health Secretary Alex Neil said this would give protection in terms of making it illegal to discriminate against anyone who refuses to participate in a same-sex marriage ceremony. A Scottish Government spokeswoman said: "It will be up to the religious body or individual celebrant to decide if they want to perform same sex marriages and there will be no obligation to opt in."