Research has described several features shared between musical rhythm and speech or language, and experimental studies consistently show associations between performance on tasks in the two domains as well as impaired rhythm processing in children with language disorders. Motivated by these results, in the current study our first aim was to explore whether a short exposure to a regular musical rhythm (i.e., rhythmic priming) can improve subsequent grammatical processing in preschool-aged Hungarian-speaking children with and without developmental language disorder (DLD). Second, we investigated whether rhythmic priming is specific to grammar processing by assessing priming in two additional domains: a linguistic but non-grammatical task (picture naming) and a non-linguistic task (nonverbal Stroop task). Third, to confirm that the rhythmic priming effect originates from the facilitating effect of the regular rhythm and not the negative effect of the control condition, we added a third condition, silence, for all the three tasks. Both groups of children showed better performance on the grammaticality judgment task in the regular compared to both the irregular and the silent conditions but no such effect appeared in the non-grammatical and non-linguistic tasks. These results suggest that (1) rhythmic priming can improve grammatical processing in Hungarian, a language with complex morphosyntax, both in children with and without DLD, (2) the effect is specific to grammar and (3) is a result of the facilitating effect of the regular rhythm. These results could motivate further research about integrating rhythmic priming into traditional speech-language therapy.