Ensembles of Deep Neural Networks, Deep Ensembles, are widely used as a simple way to boost predictive performance. However, their impact on algorithmic fairness is not well understood yet. Algorithmic fairness investigates how a model's performance varies across different groups, typically defined by protected attributes such as age, gender, or race. In this work, we investigate the interplay between the performance gains from Deep Ensembles and fairness. Our analysis reveals that they unevenly favor different groups in what we refer to as a disparate benefits effect. We empirically investigate this effect with Deep Ensembles applied to popular facial analysis and medical imaging datasets, where protected group attributes are given and find that it occurs for multiple established group fairness metrics, including statistical parity and equal opportunity. Furthermore, we identify the per-group difference in predictive diversity of ensemble members as the potential cause of the disparate benefits effect. Finally, we evaluate different approaches to reduce unfairness due to the disparate benefits effect. Our findings show that post-processing is an effective method to mitigate this unfairness while preserving the improved performance of Deep Ensembles.