Prosody is the fundamental organizing principle of spoken language, carrying lexical, morphosyntactic, and pragmatic information. It, therefore, provides highly relevant input for language development. Are infants sensitive to this important aspect of spoken language early on? In this study, we asked whether infants are able to discriminate well-formed utterance-level prosodic contours from ill-formed, backward prosodic contours at birth. This deviant prosodic contour was obtained by time-reversing the original one, and super-imposing it on the otherwise intact segmental information. The resulting backward prosodic contour was thus unfamiliar to the infants and ill-formed in French. We used near-infrared spectroscopy (NIRS) in 1-3-day-old French newborns (n = 25) to measure their brain responses to well-formed contours as standards and their backward prosody counterparts as deviants in the frontal, temporal, and parietal areas bilaterally. A cluster-based permutation test revealed greater responses to the Deviant than to the Standard condition in right temporal areas. These results suggest that newborns are already capable of detecting utterance-level prosodic violations at birth, a key ability for breaking into the native language, and that this ability is supported by brain areas similar to those in adults.