We report the first observation of the baryonic flavor-changing neutral current decay Λ(b)(0)→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 Λ(b)(0)→Λμ(+)μ(-) are measured. We find B(Λ(b)(0)→Λμ(+)μ(-))=[1.73 ± 0.42(stat) ± (syst)] × 10(-6). We also report the first measurement of the differential branching ratio of B(s)(0)→ϕμ(+)μ(-), using 49 signal events. In addition, we report branching ratios for B(+)→K(+)μ(+)μ(-), B(0)→K(0)μ(+)μ(-), and B→K(*)(892)μ(+)μ(-) decays.