The CP asymmetry in the mixing of B_{s}^{0} and B[over ¯]_{s}^{0} mesons is measured in proton-proton collision data corresponding to an integrated luminosity of 3.0  fb^{-1}, recorded by the LHCb experiment at center-of-mass energies of 7 and 8 TeV. Semileptonic B_{s}^{0} and B[over ¯]_{s}^{0} decays are studied in the inclusive mode D_{s}^{∓}μ^{±}ν[over (-)]_{μ}X with the D_{s}^{∓} mesons reconstructed in the K^{+}K^{-}π^{∓} final state. Correcting the observed charge asymmetry for detection and background effects, the CP asymmetry is found to be a_{sl}^{s}=(0.39±0.26±0.20)%, where the first uncertainty is statistical and the second systematic. This is the most precise measurement of a_{sl}^{s} to date. It is consistent with the prediction from the standard model and will constrain new models of particle physics.