The 56-second advertisement features believers from various walks of life, including the Archbishop of Canterbury Justin Welby, a weightlifter, a farmer, a couple getting married, refugees and a gospel choir, saying the main Christian prayer.
The Church of England (CofE) is the state church in England and the ad was cleared by the British Board of Film Classification and the Cinema Advertising Authority.
However, the Digital Cinema Media (DCM) agency, which handles adverts for Odeon, Cineworld and Vue cinemas, has refused to show it.
Welby, the leader of the world's Anglicans and the spiritual head of the church, said: "I find it extraordinary that cinemas rule that it is inappropriate for an advert on prayer to be shown in the week before Christmas when we celebrate the birth of Jesus Christ.
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"Billions of people across the world pray this prayer on a daily basis. I think they would be astonished and deeply saddened by this decision, especially in the light of the terrorist attack in Paris where many people have found comfort and solace in prayer.
DCM said it had a policy of "not accepting political or religious advertising content for use in its cinemas".
"Some advertisements -- unintentionally or otherwise -- could cause offence to those of differing political persuasions, as well as to those of differing faiths and indeed of no faith," it said.
"In this regard, DCM treats all political or religious beliefs equally."
CofE spokesman Reverend Arun Arora, said the decision raised questions about freedom of speech in Britain.
"The prospect of a multi-generational cultural event offered by the release of 'Star Wars: The Force Awakens' on December 18 -- a week before Christmas Day -- was too good an opportunity to miss and we are bewildered by the decision," he said.
"In one way, the decision of the cinemas is just plain silly but the fact that they have insisted upon it makes it rather chilling in terms of limiting free speech."
People should be allowed to "make up their own minds as to whether they are upset or offended by it", he said.