The differential production cross sections of ${B}^{\ifmmode\pm\else\textpm\fi{}}$ mesons are measured via the exclusive decay channels ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}{K}^{\ifmmode\pm\else\textpm\fi{}}$ as a function of transverse momentum in $p$$p$ and Pb-Pb collisions at a center-of-mass energy $\sqrt{{s}_{NN}}=5.02\text{ }\text{ }\mathrm{TeV}$ per nucleon pair with the CMS detector at the LHC. The $pp(\mathrm{Pb-Pb})$ data set used for this analysis corresponds to an integrated luminosity of $28.0\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ ($351\text{ }\text{ }\ensuremath{\mu}{\mathrm{b}}^{\ensuremath{-}1}$). The measurement is performed in the ${B}^{\ifmmode\pm\else\textpm\fi{}}$ meson transverse momentum range of 7 to $50\text{ }\text{ }\mathrm{GeV}/c$, in the rapidity interval $|y|<2.4$. In this kinematic range, a strong suppression of the production cross section by about a factor of 2 is observed in the Pb-Pb system in comparison to the expectation from $pp$ reference data. These results are found to be roughly compatible with theoretical calculations incorporating beauty quark diffusion and energy loss in a quark-gluon plasma.