We report near-surface small-angle neutron scattering (NS-SANS) and complementary off-specular neutron reflectometry (OSR) of the magnetic order in a single-crystalline epitaxial MnSi film grown on Si(111) in the thick-film limit. Providing a means of direct reciprocal space mapping, NS-SANS and OSR reveal one-dimensional magnetic modulations perpendicular to the film surface under magnetic fields parallel and perpendicular to the film surface, where additional polarized neutron reflectometry (PNR) and magnetization measurements are in excellent agreement with the literature. Regardless of the field orientation, our data does not suggest the presence of more complex spin textures, notably the formation of skyrmions. This observation establishes a distinct contrast to bulk MnSi thinned to similar nanoscale thicknesses, in which a skyrmion lattice dominates the phase diagram under perpendicular fields. Extended x-ray absorption fine structure measurements suggest that small shifts of the Si positions within the unstrained unit cell of the film control the magnetic state, representing the main structural difference between epitaxial and thinned bulk MnSi.