Isotope shifts of the 467.8 nm line have been measured by Doppler-free saturation spectroscopy for the even Cd isotopes 106 through 116. The differential changes in mean square charge radii derived from the field shifts show a pronounced break in their trend at N=64, giving evidence for the closure of the g7/2 neutron subshell. The average charge radii determined from our data and the rms radius of l~Cd measured with muonic X-rays verify the general trend predicted by the droplet model but are off by about 35 mfm on an absolute scale. A consistent interpretation of 6 (r 2) further supports the necessity for considering changes in the skin thickness of the nuclear charge distribution.