Measurements of the production of muons from heavy-flavour hadron decays in Pb–Pb collisions at s_NN=5.02 and 2.76 TeV using the ALICE detector at the LHC are reported. The nuclear modification factor R_AA at s_NN=5.02 TeV is measured at forward rapidity (2.5<y<4) as a function of transverse momentum p_T in central, semi-central, and peripheral collisions over a wide p_T interval, 3<p_T<20 GeV/c, in which muons from beauty-hadron decays are expected to take over from charm as the dominant source at high p_T (p_T>7 GeV/c). The R_AA shows an increase of the suppression of the yields of muons from heavy-flavour hadron decays with increasing centrality. A suppression by a factor of about three is observed in the 10% most central collisions. The R_AA at s_NN=5.02 TeV is similar to that at s_NN=2.76 TeV. The precise R_AA measurements have the potential to distinguish between model predictions implementing different mechanisms of parton energy loss in the high-density medium formed in heavy-ion collisions. They place important constraints for the understanding of the heavy-quark interaction with the hot and dense QCD medium.