We propose a fairness-aware learning framework that mitigates intersectional subgroup bias associated with protected attributes. Prior research has primarily focused on mitigating one kind of bias by incorporating complex fairness-driven constraints into optimization objectives or designing additional layers that focus on specific protected attributes. We introduce a simple and generic bias mitigation approach that prevents models from learning relationships between protected attributes and output variable by reducing mutual information between them. We demonstrate that our approach is effective in reducing bias with little or no drop in accuracy. We also show that the models trained with our learning framework become causally fair and insensitive to the values of protected attributes. Finally, we validate our approach by studying feature interactions between protected and non-protected attributes. We demonstrate that these interactions are significantly reduced when applying our bias mitigation.