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 $12.51\times10^{20}$ 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 $122\pm11$(stat.)$\pm15$(syst.) assuming mixing between three active flavors. No evidence for $\bar{\nu}_{\mu}\rightarrow\bar{\nu}_{s}$ 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. Comment: 8 pages, 4 figures
