  We extend to Minkowski spaces the classical result of Barbosa and do Carmo
[1] that characterizes the euclidean sphere as the unique compact stable CMC
hypersurface of $\mathbb R^n$. More precisely, if $K$ is a smooth convex body
in $\mathbb R^n$ with positive Gauss curvature, containing the origin in its
interior and $M$ is an immersed hypersurface, there are well defined concepts
of surface area measure, normal vector field and principal curvatures of $M$ ,
with respect to $K$. Thus, we introduce the concept of stability with respect
to normal variations and compute the formula of second variation with respect
to $K$. Finally we show that if $M$ is compact, has constant mean Minkowski
curvature and is stable (with respect to $K$) then $M$ is homothetic to
$\partial K$.
