  The moduli space of stable Higgs bundles of degree $0$ is equipped with the
hyperk\"ahler metric, called the Hitchin metric. On the locus where the Hitchin
fibration is smooth, there is the hyperk\"ahler metric called the semi-flat
metric, associated with the algebraic integrable systems with the Hitchin
section. We prove the exponentially rapid decay of the difference between the
Hitchin metric and the semi-flat metric along the ray $(E,t\theta)$ as
$t\to\infty$.
