A document obtained Monday from the Japan Patent Office's website said the application was made June 3 and made public June 27.
It was not immediately clear when the application might be approved. Patent office and Apple officials in Japan were not available for comment late Monday.
Apple is rumored to be working on a smart watch that would run on a version of the operating system used by its iPhone and iPad. The company has not confirmed those rumors, but CEO Tim Cook has hinted that it may be developing a wearable computing device such as a wristwatch.
Applying for a trademark in Japan isn't proof of Apple's intentions. The company based in Cupertino, California, has many patents for devices it will never produce.