  In this paper, we introduce isoparametric functions and isoparametric
hypersurfaces in Finsler manifolds and give the necessary and sufficient
conditions for a transnormal function to be isoparametric. We then prove that
hyperplanes, Minkowski hyperspheres and $F^*$-Minkowski cylinders in a
Minkowski space with $BH$-volume (resp. $HT$-volume) form are all isoparametric
hypersurfaces with one and two distinct constant principal curvatures
respectively. Moreover, we give a complete classification of isoparametric
hypersurfaces in Randers-Minkowski spaces and construct a counter example,
which shows that Wang's Theorem B in \cite{WQ} does not hold in Finsler
geometry.
