We develop a multilingual version of the Wug Test, an artificial word completion experiment that is typically used to test the morphological knowledge of children, and apply it to the GPT family of large language models (LLMs). LLMs’ performance on this test was evaluated by native speakers of six different languages, who judged whether the inflected and derived forms generated by the models conform to the morphological rules of their language. Our results show that LLMs can generalize their morphological knowledge to new, unfamiliar words, but that their success in generating the “correct” generalization (as judged by native human speakers) is predicted by a language’s morphological complexity (specifically, integrative complexity). We further find that the amount of training data has surprisingly little on LLMs’ morphological generalization abilities within the scope of the analyzed languages. These findings highlight that “morphology matters”, and have important implications for improving low-resource language modeling.