A search for B0 (s) → K0SK∗ (892)0 decays is performed using pp collision data, corresponding to an integrated luminosity of 1.0 fb−1, collected with the LHCb detector at a centre-of-mass energy of 7 TeV. The B0 s → K0 SK∗ (892)0 decay is observed for the first time, with a significance of 7.1 standard deviations. The branching fraction is measured to be B(B 0 s → K¯ 0K∗ (892)0 ) + B(B 0 s → K0K¯ ∗ (892)0 ) = (16.4 ± 3.4 ± 2.3) × 10−6 , where the first uncertainty is statistical and the second is systematic. No evidence is found for the decay B0 → K0 SK∗ (892)0 and an upper limit is set on the branching fraction, B(B0 → K¯ 0K∗ (892)0 ) + B(B0 → K0K¯ ∗ (892)0 ) < 0.96 × 10−6 , at 90 % confidence level. All results are consistent with Standard Model predictions