Interaction cross sections for ^{42-51}Ca on a carbon target at 280  MeV/nucleon have been measured for the first time. The neutron number dependence of derived root-mean-square matter radii shows a significant increase beyond the neutron magic number N=28. Furthermore, this enhancement of matter radii is much larger than that of the previously measured charge radii, indicating a novel growth in neutron skin thickness. A simple examination based on the Fermi-type distribution, and mean field calculations point out that this anomalous enhancement of the nuclear size beyond N=28 results from an enlargement of the core by a sudden increase in the surface diffuseness of the neutron density distribution, which implies the swelling of the bare ^{48}Ca core in Ca isotopes beyond N=28.