Type Ia supernovae are thought to result from a thermonuclear explosion of an accreting white dwarf in a binary system, but little is known of the precise nature of the companion star and the physical properties of the progenitor system. There are two classes of models: double-degenerate (involving two white dwarfs in a close binary system) and single-degenerate models. In the latter, the primary white dwarf accretes material from a secondary companion until conditions are such that carbon ignites, at a mass of 1.38 times the mass of the Sun. The type Ia supernova SN 2011fe was recently detected in a nearby galaxy. Here we report an analysis of archival images of the location of SN 2011fe. The luminosity of the progenitor system (especially the companion star) is 10-100 times fainter than previous limits on other type Ia supernova progenitor systems, allowing us to rule out luminous red giants and almost all helium stars as the mass-donating companion to the exploding white dwarf.