The production of ϒ(2S) and ϒ(3S) mesons in lead-lead (Pb-Pb) and proton-proton (pp) collisions is studied in their dimuon decay channel using the CMS detector at the LHC. The ϒ(3S) meson is observed for the first time in Pb-Pb collisions, with a significance above 5 standard deviations. The ratios of yields measured in Pb-Pb and pp collisions are reported for both the ϒ(2S) and ϒ(3S) mesons, as functions of transverse momentum and Pb-Pb collision centrality. These ratios, when appropriately scaled, are significantly less than unity, indicating a suppression of ϒ yields in Pb-Pb collisions. This suppression increases from peripheral to central Pb-Pb collisions. Furthermore, the suppression is stronger for ϒ(3S) mesons compared to ϒ(2S) mesons, extending the pattern of sequential suppression of quarkonium states in nuclear collisions previously seen for the J/ψ, ψ(2S), ϒ(1S), and ϒ(2S) mesons.