The first observation of the B_{s}^{0}→D[over ¯]^{0}K_{S}^{0} decay mode and evidence for the B_{s}^{0}→D[over ¯]^{*0}K_{S}^{0} decay mode are reported. The data sample corresponds to an integrated luminosity of 3.0 fb^{-1} collected in pp collisions by LHCb at center-of-mass energies of 7 and 8 TeV. The branching fractions are measured to be B(B_{s}^{0}→D[over ¯]^{0}K[over ¯]^{0})=[4.3±0.5(stat)±0.3(syst)±0.3(frag)±0.6(norm)]×10^{-4},B(B_{s}^{0}→D[over ¯]^{*0}K[over ¯]^{0})=[2.8±1.0(stat)±0.3(syst)±0.2(frag)±0.4(norm)]×10^{-4},where the uncertainties are due to contributions coming from statistical precision, systematic effects, and the precision of two external inputs, the ratio f_{s}/f_{d} and the branching fraction of B^{0}→D[over ¯]^{0}K_{S}^{0}, which is used as a calibration channel.