The differential production cross sections of B^{±} mesons are measured via the exclusive decay channels B^{±}→J/ψK^{±}→μ^{+}μ^{-}K^{±} as a function of transverse momentum in pp and Pb-Pb collisions at a center-of-mass energy sqrt[s_{NN}]=5.02  TeV per nucleon pair with the CMS detector at the LHC. The pp(Pb-Pb) data set used for this analysis corresponds to an integrated luminosity of 28.0  pb^{-1} (351  μb^{-1}). The measurement is performed in the B^{±} meson transverse momentum range of 7 to 50  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.