The perinatal period is characterized by distinct neurobiological and psychological changes initiated prenatally, which may both facilitate postpartum caregiving and increase vulnerability to stress. Parents need to adapt to the high demands of caregiving, which include responding to salient infant cues, such as infant cries. Therefore, assessing the impact of prenatal stress exposure on parents’ neural processing of infant cries may elucidate mechanisms conferring early risk for detrimental perinatal outcomes. Using event‐related potentials, we examined whether prenatal perceived stress affected neural markers of perceptual (N1, P2) and attentional (LPP) processes elicited by high‐ and low‐distress infant cries in expectant mothers (n = 38) and fathers (n = 30). Results evidenced that prenatal perceived stress impacted parents’ sustained attentional processing (LPP) of infant cries, but not early perceptual responses (N1, P2). Specifically, higher levels of prenatal perceived stress were associated with a greater LPP response to low‐distress, but not high‐distress, infant cries. There were no parental sex differences in prenatal perceived stress or neural responses to infant cries. Increased attentional processing of low‐distress cries in highly stressed parents may reflect uncertainty regarding infant distress level, thereby requiring more attentional resources. Overall, our results suggest that prenatal stress impacts processing of infant cues, even before birth.