Type Ia supernovae are thermonuclear explosions of white dwarf stars in close binary systems. They play an important role as cosmological distance indicators and have led to the discovery of the accelerated expansion of the Universe. Among the most important unsolved questions about supernovae are how the explosion actually proceeds and whether accretion occurs from a companion or by the merging of two white dwarfs. Tycho Brahe's supernova of 1572 (SN 1572) is thought to be one of the best candidates for a type Ia supernova in the Milky Way. The proximity of the SN 1572 remnant has allowed detailed studies, such as the possible identification of the binary companion, and provides a unique opportunity to test theories of the explosion mechanism and the nature of the progenitor. The determination of the hitherto unknown spectroscopic type of this supernova is crucial in relating these results to the diverse population of type Ia supernovae. Here we report an optical spectrum of Tycho's supernova near maximum brightness, obtained from a scattered-light echo more than four centuries after the direct light from the explosion swept past the Earth. We find that SN 1572 belongs to the majority class of normal type Ia supernovae.