High-velocity submicrometre-sized dust particles expelled from the jovian system have been identified by dust detectors on board several spacecraft. On the basis of periodicities in the dust impact rate, Jupiter's moon Io was found to be the dominant source of the streams. The grains become positively charged within the plasma environment of Jupiter's magnetosphere, and gain energy from its co-rotational electric field. Outside the magnetosphere, the dynamics of the grains are governed by the interaction with the interplanetary magnetic field that eventually forms the streams. A similar process was suggested for Saturn. Here we report the discovery by the Cassini spacecraft of bursts of high-velocity dust particles (> or = 100 km s(-1)) within approximately 70 million kilometres of Saturn. Most of the particles detected at large distances appear to originate from the outskirts of Saturn's outermost main ring. All bursts of dust impacts detected within 150 Saturn radii are characterized by impact directions markedly different from those measured between the bursts, and they clearly coincide with the spacecraft's traversals through streams of compressed solar wind.