Yes, China frequently restricts the content that its citizens have access to including movies from the United States. The reasons are often stated as issues of national security but they are clearly an effort to control public perception and prevent political action or awareness in its population. This type of censorship can extend to things like movies that portray a particular world view, though China pales in comparison to the censorship efforts of other nations such as North Korea.
I think most nations would have an issue with another nation making a better film about about its culture than it ever made. China will most likely ban further movies made from the U.S. The nation views itself as superior to America and is most likely insulted by the accomplishment.
A restriction won't be made based on this movie. This is because it might help the Chinese learn how to become more competitive in the movie-making industry. It is difficult to predict what China's exact advances will be, but the country is never more than a step behind anything we do in technology.
Though the national debate surrounding the Kung-Fu Panda movie relative to how Westerners produced a more authentic film about Chinese culture than the Chinese themselves my ruffle a few Chinese feathers, I do not believe China will place any restrictions on American made movies. Anything that gets their population out and into the movie theaters is probably just fine.