According to the Northampton Chronicle and Echo, a close friend of Rev Coles said he will have to miss out on the 20-date tour that starts next year.
They added: "Basically he said the Bishop of Peterborough had put the kibosh on it because the tour would interfere with his ministerial duties.
"He said the decision was out of his hands but I think he had been hoping he could have gone on it."
The friend continued, saying that the decision was even more disappointing since Rev Coles is now out of the competition.
"He brought some real humour to the dancing and it's a shame for him and his fans that they won't see him perform again," the person said.
Rev Coles conducts Sunday services at St Mary's Church in the parish of Finedon.
According to the paper, when Rt Rev Donald Allister, Bishop of Peterborough was asked why Rev Coles would not be taking part in the live tour he said: "This is a matter for Richard's judgement. I trust him and will continue to support him.
"Richard Coles sought and received goodwill for appearing on Strictly.
"His parish ministry is half-time and he has always fulfilled this commitment."
