The PHENIX experiment at the Relativistic Heavy Ion Collider has performed a systematic study of K0 S and K∗0 meson production at midrapidity in p + p, d + Au, and Cu + Cu collisions at √sNN = 200 GeV. The K0S and K∗0 mesons are reconstructed via their K0 S → π0(→ γ γ )π0(→ γ γ ) and K∗0 → K±π∓ decay modes, respectively. The measured transverse-momentum spectra are used to determine the nuclear modification factor of K0S and K∗0 mesons in d + Au and Cu + Cu collisions at different centralities. In the d + Au collisions, the nuclear modification factor of K0S 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 (K0 S , 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.