(1) Background: Home confinement and social distancing are two of the main public health measures to curb the spread of SARS-Cov-2, which can have harmful consequences on people’s mental health. This systematic review aims to identify the best available scientific evidence on the impact that home confinement and social distancing, derived from the SARS-CoV-2 pandemic, have had on the mental health of the general population in terms of depression, stress and anxiety. (2) Methods: A systematic search was conducted on PubMed, Scopus, Web of Science and ScienceDirect between 2 January 2021 and 7 January 2021, in accordance with the recommendations of the PRISMA Declaration. The selection of studies and the evaluation of their methodological quality were performed in pairs, independently and blindly, based on predetermined eligibility criteria. (3) Results: The 26 investigations reviewed were developed in different regions and countries. Factors that are associated with poor mental health were female gender, young ages, having no income and suffering from a previous psychiatric illness. Inadequate management of the pandemic by authorities and a lack or excess of information also contributed to worse mental health. (4) Conclusions: There are groups of people more likely to suffer higher levels of anxiety, depression and stress during the restrictive measures derived from COVID-19.