The single-crystal elastic properties of high-spin (Mg_0.94Fe_0.06)O ferropericlase were measured by Brillouin spectroscopy on a sample compressed to 20 GPa with diamond anvil cells using methanol-ethanol-water as a pressure-transmitting medium. At room pressure, the adiabatic bulk (K _0S) and shear (μ_0S) moduli are K _0S = 163 ± 3 GPa and μ_0S = 121 ± 2 GPa, in excellent agreement with ultrasonic results from the same bulk sample (Jacobsen et al., 2002). A fit to all our high-pressure Brillouin data using a third-order finite-strain equation of state yields the following pressure derivatives of the adiabatic bulk and shear moduli: K′_0S = 3.9 ± 0.2 and μ′_0S = 2.1 ± 0.1. Within the uncertainties, we find that K _0S and K′_0S of (Mg_0.94Fe_0.06)O are unchanged from MgO. However, μ_0S and μ′_0S of (Mg_0.94Fe_0.06)O are reduced by 8% and 11%, respectively. The aggregate compressional (V _P) and shear (V _S) wave velocities are reduced by 4% and 6%, respectively, as compared to MgO. The pressure dependence of the single-crystal elastic moduli and aggregate sound velocities is linear within the investigated pressure range. The elastic anisotropy of (Mg_0.94Fe_0.06)O is about 10% greater than that of MgO at ambient conditions. At the highest pressure obtained here, the elastic anisotropy of (Mg_0.94Fe_0.06)O is close to zero. On the basis of our measurements and earlier ultrasonic measurements, we find that the pressure derivatives of shear moduli obtained at room pressure for low iron concentrations (<20 mol% FeO) of high-spin ferropericlase are inconsistent with those inferred from the lower mantle PREM model.