"We can all feel scared sometimes just like our little owl friend Plop, but as Mrs Barn Own said, 'It's better to find out about the things that scare us before we make up our mind'.
"And with the help of others, we can often face things that worry us. Now it's time for bed. Night night and sleep tight."
It is believed Catherine enjoyed reading the full-length version of the book - which was first published in 1948 - when she was a girl and she has also shared it with her and Prince William's own children, Princes George and Louis, 8 and three, and Princess Charlotte, 6.
The duchess read the abridged version of the tale in the 10-minute segment, which was filmed in a cosy den set in her own garden in London.
Patricia Hidalgo, Director of BBC Children's and Education, said: "I couldn't be more proud to have The Duchess read a CBeebies Bedtime Story as we mark the 20th anniversary of our CBeebies and CBBC channels. It's such a special and relevant tale and perfectly represents this years' Children's Mental Health Week theme. I can't wait to see her deliver her own take on such a classic story and I'm sure our audience can't either."
Catherine is patron of children's mental health charity Place2BE and the early years is another of her big passions.
Earlier this year, she announced the development of The Royal Foundation Centre for Early Childhood, and later this month, she will be heading to Denmark as part of her work with the centre as the country is seen as a "beacon of best practice" for the 0-5 age group.