Power Laws are a characteristic distribution found in both natural as well as in man-made systems. Previous studies have shown that citations to scientific articles follow a power law, i.e., the number of papers having a certain level of citation x are proportional to x raised to some negative power. However, the distributional character of altmetrics (such as reads, likes, mentions, etc.) has not been studied in much detail, particularly with respect to existence of power law behaviours. This article, therefore, attempts to do an empirical analysis of altmetric mention data of a large set of scholarly articles to see if they exhibit power law. The individual and the composite data series of ‘mentions’ on the various platforms are fit to a power law distribution, and the parameters and goodness of fit are determined, both using least squares regression as well as the Maximum Likelihood Estimate (MLE) approach. We also explore the fit of the mention data to other distribution families like the Log-normal and exponential distributions. Results obtained confirm the existence of power law behaviour in social media mentions to scholarly articles. The Log-normal distribution also looks plausible but is not found to be statistically significant, and the exponential distribution does not show a good fit. Major implications of power law in altmetrics are given and interesting research questions are posed in pursuit of enhancing the reliability of altmetrics for research evaluation purposes.