Block-Term Tensor Regression (BTTR) has proven to be a powerful tool for modeling complex, high-dimensional data by leveraging multilinear relationships, making it particularly well-suited for applications in healthcare and neuroscience. However, traditional implementations of BTTR rely on centralized datasets, which pose significant privacy risks and hinder collaboration across institutions. To address these challenges, we introduce Federated Block-Term Tensor Regression (FBTTR), an extension of BTTR designed for federated learning scenarios. FBTTR enables decentralized data analysis, allowing institutions to collaboratively build predictive models while preserving data privacy and complying with regulations. FBTTR represents a major step forward in applying tensor regression to federated learning environments. Its performance is evaluated in two case studies: finger movement decoding from Electrocorticography (ECoG) signals and heart disease prediction. In the first case study, using the BCI Competition IV dataset, FBTTR outperforms non-multilinear models, demonstrating superior accuracy in decoding finger movements. For the dataset, for subject 3, the thumb obtained a performance of 0.76 $\pm$ .05 compared to 0.71 $\pm$ 0.05 for centralised BTTR. In the second case study, FBTTR is applied to predict heart disease using real-world clinical datasets, outperforming both standard federated learning approaches and centralized BTTR models. In the Fed-Heart-Disease Dataset, an AUC-ROC was obtained of 0.872 $\pm$ 0.02 and an accuracy of 0.772 $\pm$ 0.02 compared to 0.812 $\pm$ 0.003 and 0.753 $\pm$ 0.007 for the centralized model.