We show that in clustering dark energy models the growth index of linear matter perturbations, $\gamma$, can be much lower than in $\mathrm{\Lambda }\mathrm{CDM}$ or smooth quintessence models and presents a strong variation with redshift. We find that the impact of dark energy perturbations on $\gamma$ is enhanced if the dark energy equation of state has a large and rapid decay at low redshift. We study four different models with these features and show that we may have $0.33<\gamma (z)<0.48$ at $0<z<3$. We also show that the constant $\gamma$ parametrization for the growth rate, $f=d\ln {\delta }_m/d\ln a={\mathrm{\Omega }}_m^{\gamma }$, is a few percent inaccurate for such models and that a redshift-dependent parametrization for $\gamma$ can provide about four times more accurate fits for $f$. We discuss the robustness of the growth index to distinguish between general relativity with clustering dark energy and modified gravity models, finding that some $f(R)$ and clustering dark energy models can present similar values for $\gamma$.

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