We present a formulation of the theory of an arbitrary quantum impurity in an antiferromagnet, using the O(3) nonlinear sigma model. We obtain the low-temperature expansion for the impurity spin susceptibilities of antiferromagnets with magnetic long-range order in the ground state. We also consider the bulk quantum phase transition in d=2 to the gapped paramagnet (d is the spatial dimension): The impurity is described solely by a topological Berry phase term that is an exactly marginal perturbation to the critical theory. The physical properties of the quantum impurity near criticality are obtained by an expansion in (d-1).