The first observation of the suppressed semileptonic B 0 s → K − μ + ν μ decay is reported. Using a data sample recorded in p p collisions in 2012 with the LHCb detector, corresponding to an integrated luminosity of 2 fb − 1 , the branching fraction B ( B 0 s → K − μ + ν μ ) is measured to be [ 1.06 ± 0.05 ( stat ) ± 0.08 ( syst ) ] × 10 − 4 , where the first uncertainty is statistical and the second one represents the combined systematic uncertainties. The decay B 0 s → D − s μ + ν μ , where D − s is reconstructed in the final state K + K − π − , is used as a normalization channel to minimize the experimental systematic uncertainty. Theoretical calculations on the form factors of the B 0 s → K − and B 0 s → D − s transitions are employed to determine the ratio of the Cabibbo-Kobayashi-Maskawa matrix elements | V u b | / | V c b | at low and high B 0 s → K − momentum transfer.