A challenge towards developing NLP systems for the world's languages is understanding how they generalize to typological differences relevant for real-world applications. To this end, we propose M2C, a morphologically-aware framework for behavioral testing of NLP models. We use M2C to generate tests that probe models' behavior in light of specific linguistic features in 12 typologically diverse languages. We evaluate state-of-the-art language models on the generated tests. While models excel at most tests in English, we highlight generalization failures to specific typological characteristics such as temporal expressions in Swahili and compounding possessives in Finish. Our findings motivate the development of models that address these blind spots.