Dementia-related suicide is not well known. This study aimed to understand the characteristics of suicide risk among people with dementia and dementia family caregivers in South Korea. According to a systematic review of PRISMA guidelines, six electronic databases were searched for research published from 2010 to 2021. Ten studies were included. Among the included studies on people with dementia, one study (25%) showed no increase in the death risk of suicide, while three studies (75%) revealed suicide risk. Furthermore, in the dementia family caregivers, one study (17%) reported suicides and five studies (83%) reported suicide ideation (SI). Early dementia and independence or partial dependence in activities of daily living and home-based care are related to suicide risk in people with dementia. Meanwhile, suicide risk in dementia family caregivers is related to care burden, dementia severity, and poor approaches to coping with the family member’s dementia. The studies reviewed, which demonstrate heterogenous methodologies, suggest that both people with dementia and dementia family caregivers face suicide risk. The results of the current study offer insights useful for the prevention and treatment of mental health issues in both groups.