The PHENIX experiment at the Relativistic Heavy Ion Collider has performed a systematic study of KS0 and K*0 meson production at midrapidity in p+p,d+Au, and Cu+Cu collisions at sNN=200 GeV. The KS0 and K*0 mesons are reconstructed via their KS0→π0(→γγ)π0(→γγ) and K*0→K±π∓ decay modes, respectively. The measured transverse-momentum spectra are used to determine the nuclear modification factor of KS0 and K*0 mesons in d+Au and Cu+Cu collisions at different centralities. In the d+Au collisions, the nuclear modification factor of KS0 and K*0 mesons is almost constant as a function of transverse momentum and is consistent with unity, showing that cold-nuclear-matter effects do not play a significant role in the measured kinematic range. In Cu+Cu collisions, within the uncertainties no nuclear modification is registered in peripheral collisions. In central collisions, both mesons show suppression relative to the expectations from the p+p yield scaled by the number of binary nucleon-nucleon collisions in the Cu+Cu system. In the pT range 2–5 GeV/c, the strange mesons (KS0,K*0) similarly to the ϕ meson with hidden strangeness, show an intermediate suppression between the more suppressed light quark mesons (π0) and the nonsuppressed baryons (p,p¯). At higher transverse momentum, pT>5 GeV/c, production of all particles is similarly suppressed by a factor of ≈2.