Infants prefer to be addressed with infant-directed speech (IDS). IDS benefits language acquisition through amplified low-frequency amplitude modulations. It has been reported that this amplification increases electrophysiological tracking of IDS compared to adult-directed speech (ADS). It is still unknown which particular frequency band triggers this effect. Here, we compare tracking at the rates of syllables and prosodic stress, which are both critical to word segmentation and recognition. In mother-infant dyads (n=30), mothers described novel objects to their 9-month-olds while infants’ EEG was recorded. For IDS, mothers were instructed to speak to their children as they typically do, while for ADS, mothers described the objects as if speaking with an adult. Phonetic analyses confirmed that pitch features were more prototypically infant-directed in the IDS-condition compared to the ADS-condition. Neural tracking of speech was assessed by speech-brain coherence, which measures the synchronization between speech envelope and EEG. Results revealed significant speech-brain coherence at both syllabic and prosodic stress rates, indicating that infants track speech in IDS and ADS at both rates. We found significantly higher speech-brain coherence for IDS compared to ADS in the prosodic stress rate but not the syllabic rate. This indicates that the IDS benefit arises primarily from enhanced prosodic stress. Thus, neural tracking is sensitive to parents’ speech adaptations during natural interactions, possibly facilitating higher-level inferential processes such as word segmentation from continuous speech.