Social media sites such as Twitter is a platform where users usually express their feelings, opinions, and experiences, e.g., users often share their experiences about medications including adverse drug reactions in their tweets. Mining and detecting this information on adverse drug reactions could be immensely beneficial for pharmaceutical companies, drug-safety authorities and medical practitioners. However, the automatic extraction of adverse drug reactions from tweets is a nontrivial task due to the short and informal nature of tweets. In this paper, we aim to detect adverse drug reaction mentions in tweets where we assume that there exists a cause-effect relationship between drug names and adverse drug reactions. We propose a causality driven neural network-based approach to detect adverse drug reactions in tweets. Our approach applies a multi-head self attention mechanism to learn word-to-word interactions. We show that when the causal features are combined with the word-level semantic features, our approach can outperform several state-of-the-art adverse drug reaction detection approaches.