This Letter reports results from the first long-baseline search for sterile antineutrinos mixing in an accelerator-based antineutrino-dominated beam. The rate of neutral-current interactions in the two NOvA detectors, at distances of 1 and 810 km from the beam source, is analyzed using an exposure of 12.51×10^{20} protons-on-target from the NuMI beam at Fermilab running in antineutrino mode. A total of 121 of neutral-current candidates are observed at the far detector, compared to a prediction of 122±11(stat.)±15(syst.) assuming mixing only between three active flavors. No evidence for ν[over ¯]_{μ}→ν[over ¯]_{s} oscillation is observed. Interpreting this result within a 3+1 model, constraints are placed on the mixing angles θ_{24}<25° and θ_{34}<32° at the 90% C.L. for 0.05 eV^{2}≤Δm_{41}^{2}≤0.5 eV^{2}, the range of mass splittings that produces no significant oscillations at the near detector. These are the first 3+1 confidence limits set using long-baseline accelerator antineutrinos.