In rare event search experiments, such as those that search for dark matter particles or coherent neutrino nucleus scattering, the response of nuclear recoils are often measured directly or indirectly via an associated ionization. Nuclear recoils generate less ionization than electron recoils of the same energies, and the relative ratio, defined as the ionization yield, is crucial to calibrating the detectors. We performed a measurement of the ionization yield in silicon using a SuperCDMS-HVeV detector. By using a mono-energetic, low-energy neutron beam, and observing nuclear recoils in the HVeV detector with specific scattering angles we determined the ionization yield at six different recoil energies between 100 eV and 3.9 keV. The results deviate from the Lindhard model prediction at all energies, and are inconsistent with previous measurements below 2.3 keV, showing a higher than expected ionization yield towards lower energies.