Several works have recently focused on nonparametric active learning, especially in the binary classification setting under H\"older smoothness assumptions on the regression function. These works have highlighted the benefit of active learning by providing better rates of convergence compared to the passive counterpart. In this paper, we extend these results to multiclass classification under a more general smoothness assumption, which takes into account a broader class of underlying distributions. We present a new algorithm called \texttt{MKAL} for multiclass K-nearest neighbors active learning, and prove its theoretical benefits. Additionally, we empirically study \texttt{MKAL} on several datasets and discuss its merits and potential improvements.