The structural and magnetic properties of a cobalt nanorod array have been studied by means of magnetic field dependent small-angle neutron scattering (SANS). Measurement of the unpolarized SANS cross section dΣ/dΩ of the saturated sample in the two scattering geometries where the applied magnetic fieldHis either perpendicular or parallel to the wavevectorkiof the incoming neutron beam allows one to separate nuclear from magnetic SANS, without employing the usual sector-averaging procedure. The analysis of the SANS data in the saturated state provides structural parameters (rod radius and centre-to-centre distance) that are in good agreement with results from electron microscopy. Between saturation and the coercive field, a strong field dependence of dΣ/dΩ is observed (in both geometries), which cannot be explained using the conventional expression of the magnetic SANS cross section of magnetic nanoparticles in a homogeneous nonmagnetic matrix. The origin of the strong field dependence of dΣ/dΩ is believed to be related to intradomain spin misalignment, due to magnetocrystalline and magnetoelastic anisotropies and magnetostatic stray fields.