>>150451615
It really doesn't. Outside of the beginning, it is really isn't that comedic of a movie at all. There is some physical comedy, and Po himself as a character is a lighthearted and good-natured guy who does occasionally make jokes - but there really isn't much in the way of actual jokes in the script after Po begins his training.
For the most part, the movie takes itself mostly seriously after that point and there's far more moments that I would call heartfelt and meaningful to the characters in the last two thirds of the film than there are outright comedy sequences. Even Po's attempts at lightening the mood tend to backfire on him and the physical comedy is in service of his fighting style and personal development. Kung Fu Panda has infinitely less jokes than the majority of DreamWorks' "comedy" lineup