The aim of this systematic review was to investigate the effects of the COVID-19 lockdown on the psychological well-being of caregivers of people with dementia or mild cognitive impairment (PwD/MCI). Electronic databases were searched from inception to August 2022 for observational studies investigating the COVID-19 lockdown and psychological well-being of caregivers of PwD/MCI. Summary estimates of standardized mean differences (SMD) in psychological well-being scores pre- versus during COVID-19 were calculated using a random-effects model. Fifteen studies including 1702 caregivers (65.7% female, mean age 60.40 ± 12.9 years) with PwD/MCI were evaluated. Five studies found no change in psychological well-being parameters, including depression, anxiety, distress, caregiver burden, and quality of life. Ten studies found a worsening in at least one parameter: depression (six studies, n = 1368; SMD = 0.40; 95%CI: 0.09-0.71; p = 0.01, I(2) = 86.8%), anxiety (seven studies, n = 1569; SMD = 1.35; 95%CI: 0.05-2.65; I(2) = 99.2%), caregiver distress (six studies, n = 1320, SMD = 3.190; 95%CI: 1.42-4.95; p < 0.0001; I(2) = 99.4%), and caregiver burden (four studies, n = 852, SMD = 0.34; 95%CI: 0.13-0.56; p = 0.001; I(2) = 54.1%) (p < 0.05). There was an increase in depression, anxiety, caregiver burden, and distress in caregivers of PwD/MCI during the lockdown in the COVID pandemic. This could have longer term consequences, and it is essential that caregivers' psychological well-being is assessed and supported, to benefit both themselves and those for whom they care.