Efficient and reliable beam alignment is a critical requirement for mmWave multiple-input multiple-output (MIMO) systems, especially in 6G and beyond, where communication must be fast, adaptive, and resilient to real-world uncertainties. Existing deep learning (DL)-based beam alignment methods often neglect the underlying causal relationships between inputs and outputs, leading to limited interpretability, poor generalization, and unnecessary beam sweeping overhead. In this work, we propose a causally-aware DL framework that integrates causal discovery into beam management pipeline. Particularly, we propose a novel two-stage causal beam selection algorithm to identify a minimal set of relevant inputs for beam prediction. First, causal discovery learns a Bayesian graph capturing dependencies between received power inputs and the optimal beam. Then, this graph guides causal feature selection for the DL-based classifier. Simulation results reveal that the proposed causal beam selection matches the performance of conventional methods while drastically reducing input selection time by 94.4% and beam sweeping overhead by 59.4% by focusing only on causally relevant features.