Speaker recognition systems are widely used in various applications to identify a person by their voice; however, the high degree of variability in speech signals makes this a challenging task. Dealing with emotional variations is very difficult because emotions alter the voice characteristics of a person; thus, the acoustic features differ from those used to train models in a neutral environment. Therefore, speaker recognition models trained on neutral speech fail to correctly identify speakers under emotional stress. Although considerable advancements in speaker identification have been made using convolutional neural networks (CNN), CNNs cannot exploit the spatial association between low-level features. Inspired by the recent introduction of capsule networks (CapsNets), which are based on deep learning to overcome the inadequacy of CNNs in preserving the pose relationship between low-level features with their pooling technique, this study investigates the performance of using CapsNets in identifying speakers from emotional speech recordings. A CapsNet-based speaker identification model is proposed and evaluated using three distinct speech databases, i.e., the Emirati Speech Database, SUSAS Dataset, and RAVDESS (open-access). The proposed model is also compared to baseline systems. Experimental results demonstrate that the novel proposed CapsNet model trains faster and provides better results over current state-of-the-art schemes. The effect of the routing algorithm on speaker identification performance was also studied by varying the number of iterations, both with and without a decoder network.