It seems to work similar to clustering algorithms, where data does not have to be labeled, and the algorithm creates it's own labels/groups based on feature similarities...
While there aren't preexisting labels that trees use to distinguish all the different branching points—the branching structure is determined automatically—there does need to be a dependent variable, which generally has to be non-missing. In fact, the branching structure is determined according to how well cases are segregated on this variable. It's the presence of a dependent variable, which can be used to train and evaluate a learner, that distinguishes supervised learning from unsupervised learning.
Any method which uses training set with "correct answers" to train are, can be called as supervised learning method, and then when we put model into testing, its results are based on knowledge it gained during the training.
to develop model with Decision Tree, sufficient training examples with "correct answers" are used to train the model, i.e in supervised learning it is mandatory to have training set with correct answers to train model to get desired results.
so the Decision Tree is supervised learning