The first observation of the suppressed semileptonic Bs0→K-μ+νμ decay is reported. Using a data sample recorded in pp collisions in 2012 with the LHCb detector, corresponding to an integrated luminosity of 2 fb-1, the branching fraction B(Bs0→K-μ+νμ) 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 Bs0→Ds-μ+νμ, where Ds- 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 Bs0→K- and Bs0→Ds- transitions are employed to determine the ratio of the Cabibbo-Kobayashi-Maskawa matrix elements |Vub|/|Vcb| at low and high Bs0→K- momentum transfer.
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