The differential production cross sections of B-+/- mesons are measured via the exclusive decay channels B-+/- -> J/psi K-+/- -> mu(+)mu K--(+/-) as a function of transverse momentum in pp and Pb-Pb collisions at a center-of-mass energy root 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 mu b(-1)). The measurement is performed in the B-+/- meson transverse momentum range of 7 to 50 GeV/c, in the rapidity interval vertical bar y vertical bar < 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.