This work deals with the problem of structural disturbance decoupling by state feedback for nonlinear impulsive systems. The dynamical systems addressed exhibit a hybrid behavior characterized by a nonlinear continuous-time state evolution interrupted by abrupt discontinuities at isolated time instants. The problem considered consists in finding a state feedback such that the system output is rendered totally insensitive to the disturbance. Both the case of static state feedback and that of dynamic state feedback are considered. A necessary and sufficient condition for the existence of a static state feedback that solves the problem in the multivariable case is proven by defining suitable tools in the context of the differential geometric approach. The situation concerning solvability by a dynamic state feedback is examined in the framework of the differntial algeraic approach. A necessary and sufficient solvaility condition is conjectured and discussed.