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In this paper, we introduce the concepts of normal $m$-polar fuzzy subalgebras, maximal $m$-polar fuzzy subalgebras and completely normal $m$-polar fuzzy subalgebras in $BCK/BCI$-algebras. We discuss some properties of normal (resp., maximal, completely normal) $m$-polar fuzzy subalgebras. We prove that any non-constant normal $m$-polar fuzzy subalgebra which is a maximal element of $(\mathcal{NO}(X), \subseteq)$ takes only the values $\widehat{0}=(0, 0, ... , 0)$ and $\widehat{1}=(1, 1, ... , 1),$ and every maximal $m$-polar fuzzy subalgebra is completely normal. Moreover, we state an $m$-polar fuzzy characteristic subalgebra in $BCK/BCI$-algebras.