This work assesses one specific aspect of the relationship between auditory rhythm cognition and language skill: regularity perception. In a group of 26 adult participants, native speakers of 11 different native languages, we demonstrate a strong and significant correlation between the ability to detect a "roughly" regular beat and rapid automatized naming (RAN) as a measure of language skill (Spearman's rho, -0.47, p < 0.01). There was no such robust relationship for the "mirror image" task of irregularity detection, i.e., the ability to detect ongoing small deviations from a regular beat. The correlation between RAN and regularity detection remained significant after partialling out performance on the irregularity detection task (rho, -0.41, p, 0.022), non-verbal IQ (rho, -0.37, p < 0.05), or musical expertise (rho, -0.31, p < 0.05). Whilst being consistent with the "shared resources model" in terms of rhythm as a common basis of language and music, evolutionarily as well as in individual development, the results also document how two related rhythm processing abilities relate differently to language skill. Specifically, the results support a universal relationship between rhythmic regularity detection and reading skill that is robust to accounting for differences in fluid intelligence and musical expertise, and transcends language-specific differences in speech rhythm.