Hagos Kesete, an Eritrean pastor, says he does not want church-goers faces on television in case the authorities in the countries they have left recognise them.
The decision by the BBC to film the programme in an area of Calais known as 'The Jungle' has been met with controversy, one MP accused the broadcaster of trying to turn it into a political issue.
The 31-year-old Eriterean said: "People have a problem.
"They don't want cameras.
"If our government sees us on camera, maybe our family will have a problem."
He added that: "I have so many reasons I cannot say.
"I have fear inside.
"I am not happy to speak on video."
"The BBC has not asked me," he said in The Daily Telegraph.
He also added that appearing on the programme could endanger his family back in Eritrea.
It has been reported that a BBC camera person and three others were spotted walking around the camp over the weekend.
In Calais, this migrant camp has existed 4 months. Already people have built shops, restaurants, mosques & a church. pic.twitter.com/lgzBff8PuX
— Ari Shapiro (@arishapiro) August 6, 2015A recent report from the United Nations has condemned the government in Eritrea for its "systematic, widespread and gross human rights violations," it has also accused the government of torturing people.
Conscription in the country means that citizens are forced to join, and thousands have fled the regime.
It has also been reported to have arrested 138 Christians and church leaders as part of a crackdown on "non-traditional" Christian communities, according to the charity Open Doors.
It is thought that the congregation is mainly migrants from Eritrea and Ethiopia.
Last year Britain suspended the majority of its £27 million aid programme to Eritrea due to allegations of rape, murder and torture by the regime.
Listen to Premier's Steve Chalke speaking to Premier's Marcus Jones:
It is thought around 5,000 migrants make up 'The Jungle' at present.
Mr Kesete trained as a priest for four years, he claims he has tried to cross the border at Calais every day since his arrival at the camp a month ago: "It is very dangerous but we will still try, even if it is difficult."
Another preacher who helped to construct the church told The Daily Telegraph it was named after St Michael, the guardian angel there to "protect us all."
Soloman Grama, 39, said: "Our church is designed for all those who want to thank God for their lives and to pray for the future."
The BBC has not publicly commented on whether the broadcast will be going ahead or not.
Former Songs of Praise presenter Revd Steve Chalke has urged producers on the programme to stick with the issue, despite the ongoing contrversy.
"We talked to Catholics and we talked to Protestants at the height of some of the IRA troubles, and some people said 'I don't want to be in in this programme, I'm scarred' and that was respected and obviously this church leader's view has been respected. But I'm sure that church leader wants the issue to be known about," said Chalke.
Listen to Steve Chalke speaking to Premier's Marcus Jones:
