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 atN=64, giving evidence for the closure of theg 7/2 neutron subshell. The average charge radii determined from our data and the rms radius of114Cd 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 δ〈r 2〉 further supports the necessity for considering changes in the skin thickness of the nuclear charge distribution.