Artificial Intelligence (AI) techniques are increasingly used in computer-aided diagnostic tools in medicine. These techniques can also help to identify Hypertension (HTN) in its early stage, as it is a global health issue. Automated HTN detection uses socio-demographic, clinical data, and physiological signals. Additionally, signs of secondary HTN can also be identified using various imaging modalities. This systematic review examines related work on automated HTN detection. We identify datasets, techniques, and classifiers used to develop AI models from clinical data, physiological signals, and fused data (a combination of both). Image-based models for assessing secondary HTN are also reviewed. The majority of the studies have primarily utilized single-modality approaches, such as biological signals (e.g., electrocardiography, photoplethysmography), and medical imaging (e.g., magnetic resonance angiography, ultrasound). Surprisingly, only a small portion of the studies (22 out of 122) utilized a multi-modal fusion approach combining data from different sources. Even fewer investigated integrating clinical data, physiological signals, and medical imaging to understand the intricate relationships between these factors. Future research directions are discussed that could build better healthcare systems for early HTN detection through more integrated modeling of multi-modal data sources.