Based on low temperature resistivity, heat capacity and magnetization investigations we show that the unusually strong suppression of superconductivity in Lu$_x$Zr$_{1-x}$B$_{12}$ BSC-type superconductors in the range $x$$<$0.08 is caused by the emergence of static spin polarization in the vicinity of non-magnetic lutetium impurities. The analysis of received results points to a formation of static magnetic moments with $\mu_{eff}$$\approx$$3\mu_B$ per Lu-ion. The size of these spin polarized nanodomains was estimated to be about 5 ${\AA}$.
