Background: The lockdown due to the COVID-19 pandemic, imposed in many countries in 2021, led to social isolation and the interruption of many activities that were useful in stimulating cognition. The impact of these changes has been particularly severe in older subjects with cognitive impairment. Methods: The present study aimed to investigate the effects of lockdown on Alzheimer’s disease patients (in cognition, behavior, and autonomy) and on their caregivers (in emotions, burden, and quality of life). We created a questionnaire and performed an extensive semi-structured telephone interview with each caregiver. The main outcomes were (1) changes in cognitive and behavioral symptoms and autonomy levels in the patients and (2) effects on caregivers’ emotions, burden, and quality of life. Results: The lockdown severely impaired patients’ cognition and independence and worsened behavioral and psychological symptoms of dementia. These effects contributed to increasing caregivers’ burden and stress levels, with a significant perceived deterioration in quality of life among caregivers with higher education levels (p = 0.047). Conclusions: This study might contribute to our understanding of the impact of lockdown on Alzheimer’s disease patients and their caregivers, to guide future public health interventions aimed at preventing and/or reducing the consequences of similar extraordinary events in frail subjects.