Most existing approaches aiming at measuring trajectory similarity are focused on two‐dimensional sequences of points, called raw trajectories. However, recent proposals have used background geographic information and social media data to enrich these trajectories with a semantic dimension, giving rise to the concept of semantic trajectories. Only a few works have proposed similarity measures for semantic trajectories or multidimensional sequences, having limitations such as predefined weight of the dimensions, sensitivity to noise, tolerance for gaps with different sizes, and the prevalence of the worst dimension similarity. In this article we propose MSM, a novel similarity measure for multidimensional sequences that overcomes the aforementioned limitations by considering and weighting the similarity in all dimensions. MSM is evaluated through an extensive experimental study that, based on a seed trajectory, creates sets of semantic trajectories with controlled transformations to introduce different kinds and levels of dissimilarity. For each set, we compute the similarity between the seed and the transformed trajectories, using different measures. The results showed that MSM was more robust and efficient than related approaches in the domain of semantic trajectories.