COVID-19 represents a threat to public health and the mental health of the aged population. Prevalence and risk factors of depression and anxiety have been reported in previous reviews in other populations; however, a systematic review on the factors associated with depression and anxiety in older adults is not currently present in the literature. We searched PubMed, Embase, Scopus, ProQuest Psychology Database, Science Direct, Cochrane Library and SciELO databases (23 February 2021). The results were obtained by entering a combination of MeSH or Emtree terms with keywords related to COVID-19, elderly, depression and anxiety in the databases. A total of 11 studies were included in the systematic review. Female gender, loneliness, poor sleep quality and poor motor function were identified as factors associated with both depression and anxiety. Aspects related to having a stable and high monthly income represent protective factors for both depression and anxiety, and exercising was described as protective for depression. This study synthesised information and analysed the main factors associated with depression and anxiety in the older population during the COVID-19 pandemic. However, the cross-sectional design of most of the included studies does not allow a causal relationship between the factors analysed and depression or anxiety.