Chiral magnetic textures, such as skyrmions, are of great interest to the condensed matter community due to their novel transport properties. The stabilization of topologically non-trivial magnetic phases, like the skyrmion lattice in cubic MnSi, is governed by underlying magnetic interactions which can be probed via measurements of spin-wave excitations. Here, we report high-resolution inelastic neutron scattering (INS) measurements of the spin waves in Fe-doped Mn_(0.9)Fe_(0.1)Si deep within its field-polarized ferromagnetic state. We observe non-reciprocal spin waves with a parabolic dispersion that shifts linearly with magnetic field. Crucially, the spin-wave stiffness is highly anisotropic, with values of 17.2(5) meV~rmmathringA² parallel to the applied field and 9.3(3) meV~rmmathringA² perpendicular to it. While the applied field fundamentally lowers the systems symmetry from cubic to uniaxial, we demonstrate that the induced spin-wave anisotropy is significantly large, which is not captured within the simple theoretical approximations widely applied up to date.