M 87 is the only known non blazar radio galaxy to emit very high energy (VHE) gamma-rays. During a monitoring program of M 87, a rapid flare in VHE gamma-rays was detected by the MAGIC telescope in early 2008. The flux was found to be variable above 350 GeV on atimescaleas short as 1 day at a significance level of 5.6σ. The highest measured flux reached 15% of the Crab Nebula flux. We observed several substantial changes of the flux level during the 13 day observing period. The flux at lower energies (150-350 GeV), instead, is compatible with being constant. The energy spectrum can be described by a power law with a photon index of 2.30+/-0.11stat+/-0.20syst. The observed day-scale flux variability at VHE prefers the M 87 core as source of the emission and implies that either the emission region is very compact (just a few Schwarzschild radii) or the Doppler factor of the emitting blob is rather large in the case of a non expanding emission region.