The branching fraction of the rare B-s(0) -> phi mu(+)mu(-) decay is measured using data collected by the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV, corresponding to integrated luminosities of 1, 2, and 6 fb(-1), respectively. The branching fraction is reported in intervals of q(2), the square of the dimuon invariant mass. In the q(2) region between 1.1 and 6.0 GeV2/c(4) , the measurement is found to lie 3.6 standard deviations below a standard model prediction based on a combination of light cone sum rule and lattice QCD calculations. In addition, the first observation of the rare B-s(0)-> f(2)' (1525)mu(+)mu(-) decay is reported with a statistical significance of 9 standard deviations and its branching fraction is determined.