  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.
