Active learning has emerged as a promising approach to reduce the substantial annotation burden in 3D object detection tasks, spurring several initiatives in outdoor environments. However, its application in indoor environments remains unexplored. Compared to outdoor 3D datasets, indoor datasets face significant challenges, including fewer training samples per class, a greater number of classes, more severe class imbalance, and more diverse scene types and intra-class variances. This paper presents the first study on active learning for indoor 3D object detection, where we propose a novel framework tailored for this task. Our method incorporates two key criteria - uncertainty and diversity - to actively select the most ambiguous and informative unlabeled samples for annotation. The uncertainty criterion accounts for both inaccurate detections and undetected objects, ensuring that the most ambiguous samples are prioritized. Meanwhile, the diversity criterion is formulated as a joint optimization problem that maximizes the diversity of both object class distributions and scene types, using a new Class-aware Adaptive Prototype (CAP) bank. The CAP bank dynamically allocates representative prototypes to each class, helping to capture varying intra-class diversity across different categories. We evaluate our method on SUN RGB-D and ScanNetV2, where it outperforms baselines by a significant margin, achieving over 85% of fully-supervised performance with just 10% of the annotation budget.