We report the first observation of the baryonic flavor-changing neutral current decay Λ0b→Λμ+μ− with 24 signal events and a statistical significance of 5.8 Gaussian standard deviations. This measurement uses a pp collisions data sample corresponding to 6.8  fb−1 at s√=1.96  TeV collected by the CDF II detector at the Tevatron collider. The total and differential branching ratios for Λ0b→Λμ+μ− are measured. We find B(Λ0b→Λμ+μ−)=[1.73±0.42(stat)±(syst)]×10−6. We also report the first measurement of the differential branching ratio of B0s→ϕμ+μ−, using 49 signal events. In addition, we report branching ratios for B+→K+μ+μ−, B0→K0μ+μ−, and B→K∗(892)μ+μ− decays.