Advancements in deep learning-based 3D object detection necessitate the availability of large-scale datasets. However, this requirement introduces the challenge of manual annotation, which is often both burdensome and time-consuming. To tackle this issue, the literature has seen the emergence of several weakly supervised frameworks for 3D object detection which can automatically generate pseudo labels for unlabeled data. Nevertheless, these generated pseudo labels contain noise and are not as accurate as those labeled by humans. In this paper, we present the first approach that addresses the inherent ambiguities present in pseudo labels by introducing an Evidential Deep Learning (EDL) based uncertainty estimation framework. Specifically, we propose MEDL-U, an EDL framework based on MTrans, which not only generates pseudo labels but also quantifies the associated uncertainties. However, applying EDL to 3D object detection presents three key challenges: (1) lower pseudo label quality in comparison to other autolabelers; (2) high evidential uncertainty estimates; and (3) lack of clear interpretability and effective utilization of uncertainties for downstream tasks. We tackle these issues through the introduction of an uncertainty-aware IoU-based loss, an evidence-aware multi-task loss, and the implementation of a post-processing stage for uncertainty refinement. Our experimental results demonstrate that probabilistic detectors trained using the outputs of MEDL-U surpass deterministic detectors trained using outputs from previous 3D annotators on the KITTI val set for all difficulty levels. Moreover, MEDL-U achieves state-of-the-art results on the KITTI official test set compared to existing 3D automatic annotators. Code is publicly available at https://github.com/paathelb/MEDL-U.