Empathy is a social skill that indicates an individual's ability to understand others. Over the past few years, empathy has drawn attention from various disciplines, including but not limited to Affective Computing, Cognitive Science and Psychology. Empathy is a context-dependent term; thus, detecting or recognising empathy has potential applications in society, healthcare and education. Despite being a broad and overlapping topic, the avenue of empathy detection studies leveraging Machine Learning remains underexplored from a holistic literature perspective. To this end, we systematically collect and screen 801 papers from 10 well-known databases and analyse the selected 54 papers. We group the papers based on input modalities of empathy detection systems, i.e., text, audiovisual, audio and physiological signals. We examine modality-specific pre-processing and network architecture design protocols, popular dataset descriptions and availability details, and evaluation protocols. We further discuss the potential applications, deployment challenges and research gaps in the Affective Computing-based empathy domain, which can facilitate new avenues of exploration. We believe that our work is a stepping stone to developing a privacy-preserving and unbiased empathic system inclusive of culture, diversity and multilingualism that can be deployed in practice to enhance the overall well-being of human life.