  Let $X$ be a complex smooth projective variety such that the exterior power
of the tangent bundle $\bigwedge^{r} T_X$ is nef for some $1\leq r<\dim X$. We
prove that, up to an \'etale cover, $X$ is a Fano fiber space over an Abelian
variety. This gives generalizations of the structure theorem of varieties with
nef tangent bundle by Demailly, Peternell and Schneider and that of varieties
with nef $\bigwedge^{2} T_X$ by the author. Our result also gives an answer to
a question raised by Li, Ou and Yang for varieties with strictly nef
$\bigwedge^{r} T_X$ when $r < \dim X$.
