Cross-lingual transfer has improved greatly through multi-lingual language model pretraining, reducing the need for parallel data and increasing absolute performance. However, this progress has also brought to light the differences in performance across languages. Specifically, certain language families and typologies seem to consistently perform worse in these models. In this paper, we address what effects morphological typology has on zero-shot cross-lingual transfer for two tasks: Part-of-speech tagging and sentiment analysis. We perform experiments on 19 languages from four language typologies (fusional, isolating, agglutinative, and introflexive) and find that transfer to another morphological type generally implies a higher loss than transfer to another language with the same morphological typology. Furthermore, POS tagging is more sensitive to morphological typology than sentiment analysis and, on this task, models perform much better on fusional languages than on the other typologies.