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 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 oscillation is observed. Interpreting this result within 3 + 1 model, constraints are placed on the mixing angles and at the 90% C.L. for 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.