Offensive material according to the Agency.
The agency that handles adverts for the cinemas said it could offend those of "differing faiths and no faith".
The advert features the Christian prayer being recited or sung by a variety of people.
They include refugees, a grieving son, weightlifters at a gym, a sheep farmer, a gospel choir and the Archbishop of Canterbury, the Most Reverend Justin Welby.
'Everyday life'
The advert was passed uncut by the British Board of Film Classification and given a "U" certificate, as well as receiving clearance from the Cinema Advertising Authority.
However, the Digital Cinema Media (DCM) agency, which handles British film advertising for the major cinema chains, Odeon, Cineworld and Vue, refused to show the advert because it believed it would risk upsetting or offending audiences.
In a statement, DCM said it had a policy of not accepting political or religious advertising content in its cinemas.
It said that "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," and that "in this regard, DCM treats all political or religious beliefs equally".
The Most Reverend Justin Welby said he found the decision "extraordinary".
"This advert is about as offensive as a carol service or church service on Christmas Day," he said.
"Let the public judge for themselves rather than be censored or dictated to."
The Reverend Arun Arora, director of communications for the Church of England, said: "We find that really astonishing, disappointing and rather bewildering.
"The prospect of many families attending the release of the new Star Wars film had seemed a good opportunity to launch the advert and a new website justpray.uk to promote prayer ahead of Christmas.