We report detection of magnetar-like X-ray bursts from the young pulsar PSR J1846-0258, at the center of the supernova remnant Kes 75. This pulsar, long thought to be rotation-powered, has an inferred surface dipolar magnetic field of 4.9x10^13 G, higher than those of the vast majority of rotation-powered pulsars, but lower than those of the ~12 previously identified magnetars. The bursts were accompanied by a sudden flux increase and an unprecedented change in timing behavior. These phenomena lower the magnetic and rotational thresholds associated with magnetar-like behavior, and suggest that in neutron stars there exists a continuum of magnetic activity that increases with inferred magnetic field strength.