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 km and 810 km from the beam source, is analyzed using an exposure of $12.51times10^{20}$ 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 $122pm11$(stat.)$pm15$(syst.) assuming mixing between three active flavors. No evidence for $bar{ u}_{mu}rightarrowbar{ u}_{s}$ oscillation is observed. Interpreting this result within a 3+1 model, constraints are placed on the mixing angles ${theta}_{24} < 25^{circ}$ and ${theta}_{34} < 32^{circ}$ at the 90% C.L. for $0.05$eV$^{2} leq Delta m^{2}_{41} leq 0.5$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.
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