Core-collapse supernovae (SNe), marking the deaths of massive stars, are among the most powerful explosions in the Universe, responsible, e.g., for a predominant synthesis of chemical elements in their host galaxies. The majority of massive stars are thought to be born in close binary systems. To date, putative binary companions to the progenitors of SNe may have been detected in only two cases, SNe 1993J and 2011dh. We report on the search for a companion of the progenitor of the Type Ic SN 1994I, long considered to have been the result of binary interaction. Twenty years after explosion, we used the Hubble Space Telescope to observe the SN site in the ultraviolet (F275W and F336W bands), resulting in deep upper limits on the expected companion: F275W > 26.1 mag and F336W > 24.7 mag. These allows us to exclude the presence of a main sequence companion with a mass >~ 10 Msun. Through comparison with theoretical simulations of possible progenitor populations, we show that the upper limits to a companion detection exclude interacting binaries with semi-conservative (late Case A or early Case B) mass transfer. The limits tend to favor systems with non-conservative, late Case B mass transfer with intermediate initial orbital periods and mass ratios. The most likely mass range for a putative main sequence companion would be ~5--12 Msun, the upper end of which corresponds to the inferred upper detection limit.