Several extensions of the Standard Model contain right-handed (sterile) neutrinos in the GeV-TeV mass range. Due to their mixing with the active neutrinos, they may give rise to novel effects in cosmology, neutrino physics, and collider searches. In addition, right-handed neutrinos can also appear as final states from dark matter annihilations, with important implications for dark matter indirect detection searches. In this paper, we use current data from the Fermi Large Area Telescope (6-year observation of dwarf spheroidal galaxies) and H.E.S.S. (10-year observation of the Galactic center) to constrain the annihilation of dark matter into right-handed neutrinos. We consider right-handed neutrino with masses between 10 GeV and 1 TeV, including both two-body and three-body decays, to derive bounds on the dark matter annihilation rate, $\langle \sigma v\rangle$, as a function of the dark matter mass. Our results show, in particular, that the thermal dark matter annihilation cross section, $3\times 10^{-26}\, {\rm cm^3 s^{-1}} $, into right-handed neutrinos is excluded for dark matter masses smaller than $200$ GeV.