We present a theory of a single point, line, or plane defect coupling to th
e square of the order parameter in a metallic system near a quantum critica
l point at or above its upper critical dimension. At criticality, a spin dr
oplet is nucleated around the defect with its core size determined by the s
trength of the defect potential. Outside the core a universal slowly decayi
ng tail of the droplet is found, leading to many dissipative channels coupl
ing to the droplet and to a complete suppression of quantum tunneling. We p
ropose an NMR experiment to measure the impurity-induced changes in the loc
al spin susceptibility.