  We show that appropriately supersymmetrized smooth Maldacena-Wilson loop
operators in N=4 super Yang-Mills theory are invariant under a Yangian symmetry
Y[psu(2,2|4)] built upon the manifest superconformal symmetry algebra of the
theory. The existence of this hidden symmetry is demonstrated at the one-loop
order in the weak coupling limit as well as at leading order in the strong
coupling limit employing the classical integrability of the dual AdS_5 x S^5
string description. The hidden symmetry generators consist of a canonical
non-local second order variational derivative piece acting on the superpath,
along with a novel local path dependent contribution. We match the functional
form of these Yangian symmetry generators at weak and strong coupling and find
evidence for an interpolating function. Our findings represent the smooth
counterpart to the Yangian invariance of scattering superamplitudes dual to
light-like polygonal super Wilson loops in the N=4 super Yang-Mills theory.
