  Let $M$ be a compact complex manifold of dimension at least three and $\Pi :
M\rightarrow X$ a positive principal elliptic fibration, where $X$ is a compact
K\"ahler orbifold. Fix a preferred Hermitian metric on $M$. In \cite{V}, the
third author proved that every stable vector bundle on $M$ is of the form
$L\otimes \Pi^*B_0$, where $B_0$ is a stable vector bundle on $X$, and $L$ is a
holomorphic line bundle on $M$. Here we prove that every stable Higgs bundle on
$M$ is of the form $(L\otimes \Pi^*B_0,\Pi^*\Phi_X)$, where $(B_0, \Phi_X)$ is
a stable Higgs bundle on $X$ and $L$ is a holomorphic line bundle on $M$.
