Measurements of the branching fractions of B-s(0) -> KK-+/-(-/+) and B-s(0) -> K(+/-) pi(-/+) decays are performed using a data sample corresponding to 1.0 fb(-1) of protonproton collision data collected with the LHCb detector at a centre-of- mass energy of 7 TeV, where the K*(+/-) mesons are reconstructed in the K-s(0) pi(+/-) final state. The first observation of the B-s(0) -> K*(+/-) K--/+ decay and the first evidence for the B-s(0) -> K*(-) pi(+) decay are reported with branching fractions B(B-s(0) -> KK-+/-(-/+)) = (12.7 +/- 1.9 +/- 1.9) x 10(-6) , B(B-s(0) -> K(-) pi(+)) = (3.3 +/- 1.1 +/- 0.5) x 10(-6) , where the first uncertainties are statistical and the second are systematic. In addition, an upper limit of B(B-0 -> K*K-+/-(-/+)) < 0.4 (0.5) x 10(-6) is set at 90% (95%) confidence level.