The pastor at the church, which was the smallest at the camp, remained on the site holding a cross as bulldozers moved in.
Workers at the camp told Premier the church was not St Michaels, the building featured on the BBC's Songs of Praise.
"It's not the most famous church, St Michaels, it's the second church, which is the more Pentecostal charismatic church," Caroline Gregory from Christians for Calais told Premier.
Police had given little notice of plans to demolish the church and a nearby mosque.
Four shelters around St Michael's, the main church, were also demolished, but for the moment that church remains standing.
Ms Gregory, who has been working in the camp for some time, said: "We don't know why. We had a verbal agreement with them that they wouldn't touch any churches or mosques.
"I believe it's just part of what's happening anyway which is the gradual destroying of the camp and pushing everyone inwards."
French police have been demolishing parts of the refugee camp to create a 100 metre wide gap between the motorway and the site.
Aid agencies suspect up to 1,500 people are being forced to move.
Speaking in January, as French police announced plans to destroy parts of the camp, the Christian organisation Seeking Sanctuary told Premier it was "preposterous".