No, Taekwondo is Korean. As such, the official language if Taekwondo is Korean, and Taekwondo follows Korean traditions.
Taekwondo is heavily influenced by Karate, however, which is Japanese, which is why there are so many similarities between the two (the clothing, the belt system, many of the stances). Some of the names given to Taekwondo in its formative years were Korean pronunciations of Japanese words: Tangsudo and Gongsudo are the Korean pronunciations of Karate.
Taekwondo was developed by a number of Korean martial artists during the twentieth century, who adapted elements of Karate and a native Korean martial art called Taekkyeon. The headquarters of the World Taekwondo Federation is Kukkiwon in Seoul, the capital of South Korea.