[en] We describe the correspondence of the Matsuo–Cherednik type between the quantum n-body Ruijsenaars–Schneider model and the quantum Knizhnik–Zamolodchikov equations related to supergroup $GL(N|M)$. The spectrum of the Ruijsenaars–Schneider Hamiltonians is shown to be independent of the ${\mathbb{Z}}_2$-grading for a fixed value of $N+M$, so that $N+M+1$ different qKZ systems of equations lead to the same n-body quantum problem. The obtained results can be viewed as a quantization of the previously described quantum-classical correspondence between the classical n-body Ruijsenaars–Schneider model and the supersymmetric $GL(N|M)$ quantum spin chains on n sites.