We search for dimuon decays of a low mass particle in the decays B-0 -> K*X-0 and B-0 -> rho X-0 using a data sample of 657 x 10(6)B (B) over bar events collected with the Belle detector at the KEKB asymmetric- energy e(+)e(-) collider. We find no evidence for such a particle in the mass range from 212 MeV/c(2) to 300 MeV/c(2) for lifetimes below 10(-12) s, and set upper limits on its branching fractions. In particular, we search for a particle with a mass of 214: 3 MeV/c(2) reported by the HyperCP experiment, and obtain upper limits on the products B(B-0 -> K*X-0) x B(X mu(+)mu(-)) < 2.26(2.27) x 10(-8) and B(B-0 -> rho X-0) x B(X -> mu(+)mu(-)) < 1.73(1.73) x 10(-8) at 90% C.L. for a scalar (vector) X particle.