How does the importance of positional encoding in pre-trained language models (PLMs) vary across languages with different morphological complexity? In this paper, we offer the first study addressing this question, encompassing 23 morphologically diverse languages and 5 different downstream tasks. We choose two categories of tasks: syntactic tasks (part-of-speech tagging, named entity recognition, dependency parsing) and semantic tasks (natural language inference, paraphrasing). We consider language-specific BERT models trained on monolingual corpus for our investigation. The main experiment consists of nullifying the effect of positional encoding during fine-tuning and investigating its impact across various tasks and languages. Our findings demonstrate that the significance of positional encoding diminishes as the morphological complexity of a language increases. Across all experiments, we observe clustering of languages according to their morphological typology - with analytic languages at one end and synthetic languages at the opposite end.