The increasing deployment of distributed energy resources, renewable generation, and power-electronic converters has significantly transformed modern distribution networks. Hybrid AC/DC microgrids have emerged as an effective architecture for integrating photovoltaic generation, battery energy storage systems, and diverse load types; however, the high penetration of converter-interfaced resources and the presence of nonlinear loads introduce significant protection challenges. Fault currents in these environments often exhibit reduced magnitudes, distorted waveforms, and variable directions, limiting the effectiveness of conventional protection techniques. This paper proposes an intelligent data-driven fault detection scheme for hybrid AC/DC microgrids based on a Variational Autoencoder (VAE) and Support Vector Machine (VAE-SVM) hybrid architecture. The methodology involves extracting representative features from local electrical signals using Discrete Wavelet Transform (DWT), which are subsequently analyzed to distinguish fault conditions from normal operating states. Extensive simulation studies conducted on a 14-bus microgrid testbed demonstrate that the proposed framework achieves a fault detection accuracy of 99.25% and outperforms conventional models. Furthermore, the method exhibits high robustness against stochastic interference, maintaining a 96.45% accuracy even under severe noise conditions at a 10 dB Signal-to-Noise Ratio (SNR). The proposed scheme ensures rapid fault isolation with a total clearance time of 25 ms, providing a reliable basis for protection decisions in microgrid systems.