We report the first observation of two Cabibbo-suppressed decay modes of the Bs0 meson. Using a sample of pp̅ collisions at √s=1.96  TeV corresponding to 5.9  fb-1 of integrated luminosity collected with the CDF II, the collider detector at the Fermilab Tevatron, we search for new Bs0 decay modes in a sample of events containing J/ψ→μ+μ- decays. We reconstruct a Bs0→J/ψK*(892)0 signal with K*(892)0→K+π-, observing a yield of 151±25 events with a statistical significance of 8.0σ. We also reconstruct a Bs0→J/ψKS0 signal with KS0→π+π-, observing a yield of 64±14 events with a statistical significance of 7.2σ. From these yields, we extract the branching ratios B(Bs0→J/ψK*(892)0)=(8.3±3.8)×10-5 and B(Bs0→J/ψK0)=(3.5±0.8)×10-5, where statistical, systematic, and fragmentation-fraction uncertainties are included in the combined uncertainty.