A long-standing and unverified prediction of binary star evolution theory is the existence of a population of white dwarfs accreting from substellar donor stars. Such systems ought to be common, but the difficulty of finding them, combined with the challenge of detecting the donor against the light from accretion, means that no donor star to date has a measured mass below the hydrogen burning limit. We applied a technique that allowed us to reliably measure the mass of the unseen donor star in eclipsing systems. We were able to identify a brown dwarf donor star, with a mass of 0.052 +/- 0.002 solar mass. The relatively high mass of the donor star for its orbital period suggests that current evolutionary models may underestimate the radii of brown dwarfs.