Active learning (AL) has emerged as a crucial strategy for reducing the prohibitive costs associated with medical image segmentation. However, standard uncertainty-based AL methods typically focus on maximizing performance metrics, ignoring performance disparities or fairness across groups with sensitive attributes. While fair active learning has been explored in classification tasks, its intersection with medical image segmentation remains unaddressed. In this work, we introduced a fairness-aware active learning framework with a Weighted Entropy selection strategy that modulates uncertainty based on current group-specific performance estimates on the labeled set. To decouple true epistemic uncertainty from anatomical volume variances, we further utilized a masked, scaled entropy restricted to the region of interest. The framework was evaluated on synthetic T1-weighted brain MRIs with controlled left caudate bias in both strong and weak bias settings. A 3D U-Net was trained to segment the left caudate under several AL strategies, starting from both demographically balanced and strongly imbalanced initial labeled sets. Experiments demonstrated that our method markedly reduces performance disparities between groups compared to random sampling and standard uncertainty sampling. By prioritizing poorly segmented subgroups during the AL cycles, our method consistently achieved the highest equity-scaled performance and reduced the disparity metric by 75% (strong bias) and 86% (weak bias) relative to standard entropy at the final budget. Overall, this work is among the first studies on fair AL for medical image segmentation, offering an efficient strategy to train more equitable models in resource-constrained environments.