Soft γ-ray repeaters (SGRs) are transient sources of high-energy photons, whose brief emissions are thought to arise from young and highly magnetized neutron stars. The exact cause of these outbursts, and the nature of the energy-loss mechanism that powers them, remain unknown. Here we report the discovery of a fading radio source within the X-ray error box of SGR1900+14. We argue that the radio source is a short-lived cloud of ionized gas, powered by relativistic particles ejected at the time of the intense burst of high-energy photons in late August 1998 (this period of activity also included an extremely energetic burst of γ-rays on 27 August). As the radio photons are not beamed, our observations allow us to constrain the energy released in the form of particles ejected during the burst. Moreover, the astrometrical precision of radio observations enable us to determine the exact position of the source to very high accuracy.