Abstract : We report the first observation of the baryonic flavor-changing neutral current decay Λb0→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 6.8fb-1 at s=1.96TeV collected by the CDF II detector at the Tevatron collider. The total and differential branching ratios for Λb0→Λμ+μ- are measured. We find B(Λb0→Λμ+μ-)=[1.73±0.42(stat)±(syst)]×10-6. We also report the first measurement of the differential branching ratio of Bs0→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.