It fears Drag Queen Story Time, which has been inspired by a similar idea in the United States (pictured above), could confuse children about gender.
Ciarán Kelly, Head of Communications at the CI, said: "This has nothing to do with helping children but everything to do with using them as a propaganda tool to further the radical agenda of those who wish to do away with the precious distinctions between men and women."
Drag Queen Story Time is being developed in Birmingham and Bristol. The first even took place at an LGBT pride festival last week.
The initiative involves drag queens reading from books they enjoyed as youngsters, followed by a song with a so-called 'drag twist'.
One example includes changing words in the song 'The Wheels on the Bus' to say 'the skirt on the drag queen goes swish, swish, swish'.
Ciarán Kelly went on to say: "Children are becoming increasingly confused by teaching that constantly bombards them with the notion that they can change gender."
Drag Queen Story Time has been endorsed by the Time for Inclusive Education campaign which wants to see pro-LGBT teaching in all Scottish school.
Head of the campaign, Jordan Daly, admitted it could be "provocative or controversial for some people" but added "using drag queens like this is a fun and colourful way of challenging rigid gender stereotypes."