The compact radio source Sgr A*, believed to be the counterpart of the massive black hole at the Galactic nucleus, was observed to undergo rapid and intense flaring activity in X-rays with Chandra in October 2000. We report here the detection with XMM-Newton EPIC cameras of the early phase of a similar X-ray flare from this source, which occurred on 2001 September 4. The source 2-10 keV luminosity increased by a factor ~ 20 to reach a level of 4 10$^{34}$ erg s$^{-1}$ in a time interval of about 900 s, just before the end of the observation. The data indicate that the source spectrum was hard during the flare and can be described by simple power law of slope ~ 0.7. This XMM-Newton observation confirms the results obtained by Chandra, suggests that, in Sgr A*, rapid and intense X-ray flaring is not a rare event and therefore sets some constraints on the emission mechanism models proposed for this source.