The first observation of the decay B¯s0→D0K⁎0 using pp data collected by the LHCb detector at a centre-of-mass energy of 7 TeV, corresponding to an integrated luminosity of 36 pb−1 , is reported. A signal of 34.4±6.8 events is obtained and the absence of signal is rejected with a statistical significance of more than nine standard deviations. The B¯s0→D0K⁎0 branching fraction is measured relative to that of B¯0→D0ρ0 : B(B¯s0→D0K⁎0)B(B¯0→D0ρ0)=1.48±0.34±0.15±0.12 , where the first uncertainty is statistical, the second systematic and the third is due to the uncertainty on the ratio of the B0 and Bs0 hadronisation fractions.