Little is known about language development after late-to-moderate premature birth, the most significant part of prematurity worldwide. We examined minimal-pair word-learning skills in 18 eighteen-month-old healthy full-term (mean gestational age [GA] at birth = 39.6 weeks; 7 males; 100% Caucasian) and 18 healthy late-to-moderate preterm infants (mean GA at birth 33.7 weeks; 11 males; 100% Caucasian). Data were collected in the local urban area of Barcelona city from May 2015 to August 2016. Toddlers first associated two pseudo-words, forming a minimal pair based on a voice onset time distinction of the initial consonant, with two unfamiliar objects during a habituation phase. A visual choice test assessed their recognition of the two novel word-object associations and some familiar word-object pairs. While full-terms successfully mapped the similar sounding pair of novel words (d = 1.57), preterms could not (d = 0.17). These results suggest that late to moderate preterm birth can hinder basic associative learning mechanisms relying on fine temporal speech features.