Previous studies show that verbal short-term memory (VSTM) is related to vocabulary learning, whereas verbal working memory (VWM) is related to grammar learning in children learning a second language (L2) in the classroom. In this study, we investigated whether the same relationships apply to children learning an L2 in a naturalistic setting and to monolingual children. We also investigated whether relationships with verbal memory differ depending on the type of grammar skill investigated (i.e., morphology vs. syntax). Participants were 63 Turkish children who learned Dutch as an L2 and 45 Dutch monolingual children (mean age = 5 years). Children completed a series of VSTM and VWM tasks, a Dutch vocabulary task, and a Dutch grammar task. A confirmatory factor analysis showed that VSTM and VWM represented two separate latent factors in both groups. Structural equation modeling showed that VSTM, treated as a latent factor, significantly predicted vocabulary and grammar. VWM, treated as a latent factor, predicted only grammar. Both memory factors were significantly related to the acquisition of morphology and syntax. There were no differences between the two groups. These results show that (a) VSTM and VWM are differentially associated with language learning and (b) the same memory mechanisms are employed for learning vocabulary and grammar in L1 children and in L2 children who learn their L2 naturalistically.