The element vertical bar V-cb vertical bar of the Cabibbo-Kobayashi-Maskawa matrix is measured using semileptonic B-s(0) decays produced in proton-proton collision data collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3 fb(-1). Rates of B-s0 -> D-s(-) mu(+)nu(mu) and B-s0 -> D-s*(-) mu(+)nu(mu) decays are analyzed using hadronic form-factor parametrizations derived either by Caprini, Lellouch and Neubert (CLN) or by Boyd, Grinstein and Lebed (BGL). The measured values of vertical bar V-cb vertical bar are (41.4 +/- 0.6 +/- 0.9 +/- 1.2) x 10(-3) and (42.3 +/- 0.8 +/- 0.9 +/- 1.2) x 10(-3) in the CLN and BGL parametrization, respectively. The first uncertainty is statistical, the second systematic, and the third is due to the external inputs used in the measurement. These results are in agreement with those obtained from decays of B+ and B-0 mesons. They are the first determinations of vertical bar V-cb vertical bar at a hadron-collider experiment and the first using B-s(0) meson decays.