The current study examined whether adults with Developmental Dyslexia are impaired in learning linguistic regularities in a novel language, and whether this may be explained by a domain general deficit in the effect of sleep on consolidation. We compared online learning and offline consolidation of morphological regularities in individuals with Developmental Dyslexia (N = 40) and typical readers (N = 38). Participants learned to apply plural inflections to novel words based on morpho-phonological rules embedded in the input and learned to execute a finger motor sequence task. To test the effects of time and sleep on consolidation, participants were assigned into one of two sleep-schedule groups, trained in the evening or in the morning and tested 12 and 24 h later. Unlike typical readers, Dyslexic readers did not extract the morpho-phonological regularities during training and as a group they did not show offline gains in inflecting trained items 24 h after training, suggesting that the deficit in extraction of regularities during training may be related to the deficit in consolidation. The offline gains in dyslexic readers, were correlated with their prior phonological abilities, and were less affected by sleep than those of typical readers. Although no deficit was found in the consolidation of the motor task, dyslexic readers were again less successful in generating an abstract representation of the motor sequence, reflected in a difficulty to generalize the motor sequence knowledge acquired using one hand to the untrained hand. The results suggest that individuals with Developmental Dyslexia have a domain general deficit in extracting statistical regularities from an input. Within the language domain this deficit is reflected in reduced benefits of consolidation, particularly during sleep, perhaps due to reduced prior phonological abilities, which may impede the individual's ability to extract the linguistic regularities during and after training and thus constrain the consolidation process.