We report a search for charmless hadronic decays of neutral B mesons to eta ' K* (892)(0). The results are based on a 711 fb(-1) data sample that contains 772 x 10(6) B (B) over bar pairs, collected at the gamma(4S) resonance with the Belle detector at the KEKB asymmetric energy e(+)e(-) collider. We observe the decay for the first time with a significance of 5.0 standard deviations and obtain its branching fraction B[B-0 -> eta ' K* (892)(0)] = [2.6 +/- 0.7(stat) +/- 0.2(syst)] x 10(-6). We also measure the CP-violating asymmetry as A(CP) [B-0 -> eta ' K* (892)(0)] = -0.22 +/- 0.29(stat) +/- 0.07(syst).