We report first observations of B-s(0) -> J/psi eta and B-s(0) -> J/psi eta'. The results are obtained from 121.4 fb(-1) of data collected at the Gamma(5S) resonance with the Belle detector at the KEKB e(+)e(-) collider. We obtain the branching fractions B(B-s(0)-> J/psi eta')=[5.10 +/- 0.50(stat)+/- 0.25(syst)(-0.79)(+1.14)(N-Bs()(B) over bars()] X 10(-4,) B(B-s(0)-> J/psi eta') = [3.71 +/- 0.61(stat)+/-(+0.83)(-0.57)(N-Bs()(B) over bars()] X 10(-4). The ratio of the two branching fractions is measured to be B(B-s -> J/psi eta')/B(B-s -> J/psi eta) = 0.73 +/- 0.14(stat) +/- 0.02(syst).