Sgr A*, the compact radio source 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 2000 October. We report here the detection with XMM-Newton European Photon Imaging 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 of≈ 20 to reach a level of 4× 10 34 ergs 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. This XMM-Newton observation confirms the results obtained by Chandra and suggests that in Sgr A* rapid and intense X-ray flaring is not a rare event. This can constrain the emission mechanism models proposed for this source and also implies that the crucial multiwavelength observation programs planned to explore the behavior of the radio/submillimeter and hard X-ray/gamma-ray emissions during the X-ray flares have a good chance of success.