Chloroquine (CQ) and hydroxychloroquine (HCQ) are classical anti-malarial and anti-inflammatory treatments, which were used as first-line therapy at the beginning of the 2019 coronavirus disease (COVID-19) pandemic. Besides the emerging data on their lack of efficacy against COVID-19 infection, such treatments have been associated with some severe health concerns, including those of neuropsychiatric nature, such as a possible increase in suicide risk. Here we report a case of a patient with no history of psychiatric illnesses, who abruptly developed depression with melancholic features, severe suicidal ideation (SI), and attempted suicide (SA) shortly after receiving HCQ for his COVID-19 infection. The case was followed by a mini-review of the heterogeneous scientific literature on the hypothetical association between neuropsychiatric symptoms, with a focus on SI and suicidal behavior (SB, including SA and death by suicide), when CQ and HCQ are used in COVID-19, rheumatologic diseases, and malaria settings. Considering the anti-inflammatory properties of CQ and HCQ and the implications for neuroinflammation in suicide pathogenesis, the possible increase in suicide risk caused by these medications appears paradoxical and suggests that other underlying pathological trajectories might account for this eventuality. In this regard, some of these latter mechanistic postulates were proposed. Certainly the role and contribution of psycho-social factors that a COVID-19 patient had to face can neither be minimized nor excluded in the attempt to understand his suffering until the development of SI/SB. However, while this case report represents a rare scenario in clinical practice and no consensus exists in the literature on this topic, a psychiatric screening for suicide risk in patients using of CQ and HCQ could be carefully considered.