For the first time an excess of photons above an energy threshold of 730 GeV from the giant radio galaxy M 87 has been measured at a significance level above 4 σ. The data have been taken during the years 1998 and 1999 with the HEGRA stereoscopic system of 5 imaging atmospheric Cherenkov telescopes. The excess of 107.4 ± 26.8 events above 730 GeV corresponds to an integral flux of 3.3% of the Crab flux or Nγ (E > 730 GeV) = (0.96 ± 0.23) × 10-12 phot cm-2 s-1. M 87 is located at the center of the Virgo cluster of galaxies at a relatively small redshift of z = 0.00436 and is a promising candidate among the class of giant radio galaxies for the emission of TeV γ-radiation. The detection of TeV γ-rays from M 87 - if confirmed - would establish a new class of extragalactic source in this energy regime since all other AGN detected to date at TeV energies are BL Lac type objects.