Driven by gravity, massive structures like galaxies and clusters of galaxies are believed to grow continuously through hierarchical merging and accretion of smaller systems. Observational evidence of accretion events is provided by the coherent stellar streams crossing the outer haloes of massive galaxies, such as the Milky Way(1) or Andromeda(2). At similar mass scales, around 1011 solar masses in stars, further evidence of merging activity is also ample(3-5). Mergers of lower-mass galaxies are expected within the hierarchical process of galaxy formation(6), but have hitherto not been seen for galaxies with less than about 10(9) solar masses in stars(7,8). Here we report the kinematic detection of a stellar stream in one of the satellite galaxies of Andromeda, the dwarf spheroidal Andromeda II, which has a mass of only 10(7) solar masses in stars(9). The properties of the stream show that we are observing the remnant of a merger between two dwarf galaxies. This had a drastic influence on the dynamics of the remnant, which is now rotating around its projected major axis(10). The stellar stream in Andromeda II illustrates the scale-free character of the formation of galaxies, down to the lowest galactic mass scales.