Estimating the camera's pose given images from a single camera is a traditional task in mobile robots and autonomous vehicles. This problem is called monocular visual odometry and often relies on geometric approaches that require considerable engineering effort for a specific scenario. Deep learning methods have been shown to be generalizable after proper training and with a large amount of available data. Transformer-based architectures have dominated the state-of-the-art in natural language processing and computer vision tasks, such as image and video understanding. In this work, we deal with the monocular visual odometry as a video understanding task to estimate the 6 degrees of freedom of a camera's pose. We contribute by presenting the TSformer-VO model based on spatio-temporal self-attention mechanisms to extract features from clips and estimate the motions in an end-to-end manner. Our approach achieved competitive state-of-the-art performance compared with geometry-based and deep learning-based methods on the KITTI visual odometry dataset, outperforming the DeepVO implementation highly accepted in the visual odometry community. The code is publicly available at https://github.com/aofrancani/TSformer-VO.