The recent detection in archival Hubble Space Telescope images of an object at the location of supernova (SN) iPTF13bvn may represent the first direct evidence of the progenitor of a Type Ib SN. The object's photometry was found to be compatible with a Wolf-Rayet pre-SN star mass of approximate to 11 M-circle dot. However, based on hydrodynamical models, we show that the progenitor had a pre-SN mass of approximate to 3.5 M-circle dot and that it could not be larger than approximate to 8 M-circle dot. We propose an interacting binary system as the SN progenitor and perform evolutionary calculations that are able to self-consistently explain the light curve shape, the absence of hydrogen, and the pre-SN photometry. We further discuss the range of allowed binary systems and predict that the remaining companion is a luminous O-type star of significantly lower flux in the optical than the pre-SN object. A future detection of such a star may be possible and would provide the first robust identification of a progenitor system for a Type Ib SN.