The production of non-prompt $\rm D^0$ mesons from beauty-hadron decays was measured at midrapidity ($|y| < 0.5$) in Pb-Pb collisions at a nucleon-nucleon center-of-mass energy of $\sqrt{s_{\text{NN}}}=5.02$ TeV with the ALICE experiment at the LHC. Their nuclear modification factor ($R_{\rm AA}$), measured for the first time down to $p_{\rm T}$ = 1 GeV/$c$  in the 0-10% and 30-50% centrality classes, indicates a significant suppression, up to a factor of about three, for $p_{\rm T}$ > 5 GeV/$c$ in the 0-10% central Pb--Pb collisions.The data are described by models that include both collisional and radiative processes in the calculation of beauty-quark energy loss in the quark--gluon plasma, and quark recombination in addition to fragmentation as a hadronization mechanism. The ratio of the non-prompt to prompt $\rm D^0$-meson $R_{\rm AA}$ is larger than unity for $p_{\rm T}$ > 4 GeV/$c$ in the 0-10% central Pb-Pb collisions, as predicted by models in which beauty quarks lose less energy than charm quarks in the quark-gluon plasma because of their larger mass.