Auditory speech discrimination is essential for normal language development. Children born preterm are at greater risk of language developmental delays. Using functional near-infrared spectroscopy at term-equivalent age, the present study investigated early discrimination of speech prosody in 62 neonates born between week 23 and 41 of gestational age (GA). We found a significant positive correlation between GA at birth and neural discrimination of forward versus backward speech at term-equivalent age. Cluster analysis identified a critical threshold at around week 32 of GA, pointing out the existence of subgroups. Infants born before week 32 of GA exhibited a significantly different pattern of hemodynamic response to speech stimuli compared to infants born at or after week 32 of GA. Thus, children born before the GA of 32 weeks are especially vulnerable to early speech discrimination deficits. To support their early language development, we therefore suggest a close follow-up and additional speech and language therapy especially in the group of children born before week 32 of GA.