Irony is a kind of figurative language used by a speaker to say something that contrasts with the context and, to some extent, lends humor to a situation. However, little is known about the brain regions that specifically support the processing of these two common features of irony. The present study had two main aims: (i) investigate the neural basis of irony processing, by delivering short ironic spoken sentences (and their literal counterparts) to participants undergoing fMRI; and (ii) assess the neural effect of two irony parameters, obtained from normative studies: degree of contrast and humor appreciation. Results revealed activation of the bilateral inferior frontal gyrus (IFG), posterior part of the left superior temporal gyrus, medial frontal cortex, and left caudate during irony processing, suggesting the involvement of both semantic and theory-of-mind networks. Parametric models showed that contrast was specifically associated with the activation of bilateral frontal and subcortical areas, and that these regions were also sensitive to humor, as shown by a conjunction analysis. Activation of the bilateral IFG is consistent with the literature on humor processing, and reflects incongruity detection/resolution processes. Moreover, the activation of subcortical structures can be related to the reward processing of social events.