We report results from the first search for sterile neutrinos mixing with active neutrinos through a reduction in the rate of neutral-current interactions over a baseline of 810\,km between the NOvA detectors. Analyzing a 14-kton detector equivalent exposure of 6.05$\times$10$^{20}$ protons-on-target in the NuMI beam at Fermilab, we observe 95 neutral-current candidates at the Far Detector compared with $83.5 \pm 9.7 \mbox{(stat.)} \pm 9.4 \mbox{(syst.)}$ events predicted assuming mixing only occurs between active neutrino species. No evidence for $\nu_{\mu} \rightarrow \nu_{s}$ transitions is found. Interpreting these results within a 3+1 model, we place constraints on the mixing angles $\theta_{24}<20.8^{\circ}$ and $\theta_{34}<31.2^{\circ}$ 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 produce no significant oscillations over the Near Detector baseline. Comment: 8 pages, 4 figures
