We perform an extensive analysis of the low-degree gravity field harmonics measured by the GRACE mission, in order to find a signature of the postseismic relaxation following the 2004 Sumatra earthquake. We find a statistically significant perturbation in the secular trend of low-degree zonal coefficients (J _l ) in correspondence of the 2004 Sumatra earthquake and a similar perturbation, but with weak associated statistical significance, also in the nonzonal coefficients. Technical features and results of such analysis are discussed. The time-dependent postseismic evolution of harmonic coefficients is modeled for various asthenosphere viscosity values, using a theoretical model of global postseismic deformation. The observed change in secular trend is found to be consistent with our modeling results but it cannot be used to discriminate between viscosities. A forward modeling of the perturbations to time-dependent zonal variation rates following the Sumatra earthquake for various asthenospheric viscosities is provided. As a result, an evident signature of the Sumatra earthquake on _l time series is expected for asthenospheric viscosity values below 10¹⁸ Pa s. Therefore, long term _l time histories from satellite laser ranging will be able to put constraints on the asthenosphere viscosity, if such a signature is evidenced from data or, at least, put lower limits if no significant perturbation will be observed.