In this paper we consider the evolution of small planetesimals (radii similar to1-10 m) in marginally stable, self-gravitating protoplanetary discs. The drag force between the disc gas and the embedded planetesimals generally causes the planetesimals to drift inwards through the disc at a rate that depends on the particle size. In a marginally stable, self-gravitating disc, however, the planetesimals are significantly influenced by the non-axisymmetric spiral structures resulting from the growth of the gravitational instability. The drag force now causes the planetesimals to drift towards the peaks of the spiral arms where the density and pressure are highest. For small particles that are strongly coupled to the disc gas, and for large particles that have essentially decoupled from the disc gas, the effect is not particularly significant. Intermediate-sized particles, which would generally have the largest radial drift rates, do, however, become significantly concentrated at the peaks of the spiral arms. These high-density regions may persist for, of order, an orbital period and may attain densities comparable to that of the disc gas. Although at the end of the simulation only 25 per cent of the planetesimal particles lie in regions of enhanced density, during the course of the simulation at least 75 per cent of the planetesimal particles have at some stage been in a such a region. We find that the concentration of particles in the spiral arms results in an increased collision rate, an effect that could significantly accelerate planetesimal growth. The density enhancements may also be sufficient for the growth of planetesimals through direct gravitational collapse. The interaction between small planetesimals and self-gravitating spiral structures may therefore play an important role in the formation of large planetesimals that will ultimately coagulate to form terrestrial planets or the cores of gas/ice giant planets.