The Beatles legend says Beatrice - his child with estranged wife Heather Mills - is a huge fan of the popular animated film series and loves it when her famous dad impersonates the green "Scottish" ogre.
McCartney said: "I'm a huge fan of 'Shrek' as my little girl, who is three, loves it. I can do a really good impression of him - I put on my best Scottish accent!"
The 65-year-old musician also revealed he has a phobia of putting things in his ears.
McCartney owns an Apple iPod MP3 player but rarely uses it because earphones remind him of being at work.
He said: "I've got an iPod but I don't really like sticking the headphones in my ears. It just reminds me too much of being at work, being in the studio."
"I love what they can do, the way they store music, but I tend to listen to music when I'm in my car."
