Traditional radio map estimation (RME) techniques fail to capture multi-dimensional and dynamic characteristics of complex spectrum environments. Recent data-driven methods achieve accurate RME in spatial domain, but ignore physical prior knowledge of radio propagation, limiting data efficiency especially in multi-dimensional scenarios. To overcome such limitations, we propose a new foundation model, characterized by self-supervised pre-training on diverse data for zero-shot generalization, enabling multi-dimensional radio map estimation (FM-RME). Specifically, FM-RME builds an effective synergy of two core components: a geometry-aware feature extraction module that encodes physical propagation symmetries, i.e., translation and rotation invariance, as inductive bias, and an attention-based neural network that learns long-range correlations across the spatial-temporal-spectral domains. A masked self-supervised multi-dimensional pre-training strategy is further developed to learn generalizable spectrum representations across diverse wireless environments. Once pre-trained, FM-RME supports zero-shot inference for multi-dimensional RME, including spatial, temporal, and spectral estimation, without scenario-specific retraining. Simulation results verify that FM-RME exhibits desired learning performance across diverse datasets and zero-shot generalization capabilities beyond existing RME methods.