Models with dark energy decaying into dark matter have been proposed to solve the coincidence problem in cosmology.We study the effect of such coupling in the matter power spectrum. Because of the interaction, the growth of matter density perturbations during the radiation dominated regime is slower compared to noninteracting models with the same ratio of dark matter to dark energy today. This effect introduces a damping on the power spectrum at small scales proportional to the strength of the interaction, c2, and similar to the effect generated by ultrarelativistic neutrinos. The interaction also shifts matterradiation equality to larger scales. We compare the matter power spectrum of interacting quintessence models with the measurments of the 2-degree field galaxy redshift survey (2dFGRS). The data are insensitive to values of c2 ≤ 10-3 but strongly constrain larger values. We particularize our study to models that during radiation domination have a constant dark matter to dark energy ratio.