  We investigate the growth of matter fluctuations in holographic dark energy
cosmologies. First we use an overall statistical analysis involving the latest
observational data in order to place constraints on the cosmological
parameters. Then we test the range of validity of the holographic dark energy
models at the perturbation level and its variants from the concordance
$\Lambda$ cosmology. Specifically, we provide a new analytical approach in
order to derive, for the first time, the growth index of matter perturbations.
Considering a homogeneous holographic dark energy we find that the growth index
is $\gamma \approx \frac{4}{7}$ which is somewhat larger ($\sim 4.8\%$) than
that of the usual $\Lambda$ cosmology, $\gamma^{(\Lambda)}\approx
\frac{6}{11}$. Finally, if we allow clustering in the holographic dark energy
models then the asymptotic value of the growth index is given in terms of the
effective sound speed $c_{\rm eff}^2$, namely $\gamma \approx \frac{3(1-c_{\rm
eff}^2)}{7}$.
