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 x 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 (v) over bar (mu)-> (v) over bar (s) oscillation is observed. Interpreting this result within a 3 + 1 model, constraints are placed on the mixing angles theta(24) < 25 degrees and theta(34) < 32 degrees at the 90% C.L. for 0.05 eV(2) <= Delta m(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.