We report on a search for low mass companions within 10 AU of the star Fomalhaut, using narrowband observations at 4.05 mu m obtained with the Apodizing Phase Plate coronagraph on the VLT/NaCo. Our observations place a model-dependent upper mass limit of 12-20 M-jup from 4 to 10 AU, covering the semimajor axis search space between interferometric imaging measurements and other direct imaging non-detections. These observations rule out models where the large semimajor axis for the putative candidate companion Fomalhaut b is explained by dynamical scattering from a more massive companion in the inner stellar system, where such giant planets are thought to form.