Type Ia supernovae have proven vital to our understanding of cosmology, both as standard candles and for their role in galactic chemical evolution; however, their origin remains uncertain. The canonical accretion model implies a hot and luminous progenitor that would ionize the surrounding gas out to a radius of ~10-100 pc for ~100,000 years after the explosion. Here, we report stringent upper limits on the temperature and luminosity of the progenitor of Tycho's supernova (SN 1572), determined using the remnant itself as a probe of its environment. Hot, luminous progenitors that would have produced a greater hydrogen ionization fraction than that measured at the radius of the present remnant (~3 pc) can thus be excluded. This conclusively rules out steadily nuclear-burning white dwarfs (supersoft X-ray sources), as well as disk emission from a Chandrasekhar-mass white dwarf accreting approximately greater than 10-8 M · yr-1 (recurrent novae; M · is equal to one solar mass). The lack of a surrounding Strömgren sphere is consistent with the merger of a double white dwarf binary, although other more exotic scenarios may be possible.