Due to their proximity, high dark-matter (DM) content, and apparent absence of non-thermal processes, Milky Way dwarf spheroidal satellite galaxies (dSphs) are excellent targets for the indirect detection of DM. Recently, eight new dSph candidates were discovered using the first year of data from the Dark Energy Survey (DES). We searched for gamma-ray emission coincident with the positions of these new objects in six years of Fermi Large Area Telescope data. We found no significant excesses of gamma-ray emission. Under the assumption that the DES candidates are dSphs with DM halo properties similar to the known dSphs, we computed individual and combined limits on the velocity-averaged DM annihilation cross section for these new targets. If the estimated DM content of these dSph candidates is confirmed, they will constrain the annihilation cross section to lie below the thermal relic cross section for DM particles with masses 20 GeV annihilating via the bb¯ or τ+τ− channels