The COVID-19 pandemic had imposed a variety of containment measures on the general population for prolonged periods. Confinement has had, and still has, social, economic, educational, health, and psychological consequences on the entire population. Objective: In this article, a systematic search has been performed based on studies carried out since the beginning of the pandemic, regarding the impact of these containment measures on the autism spectrum disorder (ASD) population and their caregivers. Method: We consulted six databases (i.e., PubMed, Medline, Embase, Scopus, Web of Science, and Science Direct) and selected ten studies that met the inclusion criteria. The chosen studies have been classified according to their theoretical focus, methodology, and target population. Results: We found an increase in stress and a decrease in psychological well-being among individuals diagnosed with ASD (i.e., parents and caregivers). Additionally, in studies focused on children, youth, and adults with ASD diagnosis, the results are contradictory depending on variables such as age, ASD severity, or type of family structure. Conclusions: The results show that the consequences of quarantine and social confinement are quite contradictory and depend on variables such as age, ASD severity, and family features.