The exhaust plume of the Space Shuttle during its ascent is a very powerful source of energy that excites atmospheric acoustic perturbations. Because of the coupling between neutral particles and electrons at ionospheric altitudes, these low frequency acoustic perturbations induce variations of the ionospheric electron density. We computed ionospheric electron content time series using Global Positioning System data collected on Bermuda island during the STS-58 Space Shuttle launch. The analysis of these time series shows a perturbation of the ionospheric electron content following the launch and lasting for 35 mn, with periods less than 10 mn. The perturbation is complex and shows two sub-events separated by about 15 mn at 200 km from the source. The phase velocities and waveform characteristics of the two sub-events lead us to interpret the first impulsive arrival as the direct propagation of the shock wave front, followed by oscillatory guided waves probably excited by the primary shock wave and propagating along horizontal atmospheric interfaces at 120 km altitude and below.