Autism Spectrum Disorder (ASD) is a neuro-developmental disorder that limits social interactions, cognitive skills, and abilities. Since ASD can last during an affected person's entire life cycle, the diagnosis at the early onset can yield a significant positive impact. The current medical diagnostic systems (e.g., DSM-5/ICD-10) are somewhat subjective; rely purely on the behavioral observation of symptoms, and hence, some individuals often go misdiagnosed or late-diagnosed. Therefore, researchers have focused on developing data-driven automated diagnosis systems with less screening time, low cost, and improved accuracy while significantly reducing professional intervention. Human Activity Analysis (HAA) is considered one of the most promising niches in computer vision research. This paper aims to analyze its potentialities in the automated detection of autism by tracking the exclusive characteristics of autistic individuals such as repetitive behavior, atypical walking style, and unusual visual saliency. This review provides a detailed inspection of HAA-based autism detection literature published in 2011 on-wards depicting core approaches, challenges, probable solutions, available resources, and scopes of future exploration in this arena. According to our study, deep learning outperforms machine learning in ASD detection with a classification accuracy of 76\% to 95\% on different datasets comprise of video, image, or skeleton data that recorded participants performing a large number of actions. However, machine learning provides satisfactory results on datasets with a small number of action classes and has a range of 60\% to 93\% accuracy among numerous studies. We hope this extensive review will provide a comprehensive guideline for researchers in this field.