The paper reports on the first experimental evidence for space-observed manifestation of the open ocean tsunami in the microwave radar backscatter (in C- and Ku-bands; electromagnetic wave lengths 6cm and 2 cm respectively). Significant (a few dB) variations of the radar cross section synchronous with the sea level anomaly were found in the geophysical data record of the altimetry satellite Jason-1 for the track which crossed the head wave of the catastrophic tsunami of 26 December 2004. The simultaneous analysis of the available complementary data provided by the satellite three-channel radiometer enabled us to exclude meteorological factors as possible causes of the observed signal modulation. A possible physical mechanism of modulation of short wind waves due to transformation of the thin boundary layer in the air by a tsunami wave is discussed. The results open new possibilities of monitoring tsunamis from space.