(1) Background: This study aimed to evaluate the feasibility of a telehealth home-based exercise program for older people with dementia living in Indonesia with support from their informal carers. (2) Methods: Pre–post intervention single group study with three assessment time-points (baseline, 12 and 18 weeks). Participants with dementia underwent a 12-week physiotherapist-delivered telehealth exercise program, with informal carer supervision between supervised online sessions, and continued the exercises for a further six weeks without physiotherapist online supervision. (3) Results: Thirty dyads of older people with dementia and their informal carers were recruited; four (13.3%) withdrew across the 12-week intervention and one (3.3%) in the 6-week self-maintenance period. Median adherence was 84.1% (IQR [25, 75] = 17.1) during the 12-week intervention, and 66.7% (IQR [25, 75] = 16.7) in the self-maintenance period. No falls/adverse events were reported. Physical activity level, some aspects of function and disability, health-related benefits of exercise, exercise enjoyment and quality of life of older people with dementia improved significantly at 12 and 18 weeks. (4) Conclusions: The telehealth exercise program is feasible and safe and may have benefits for the health outcomes of community-living older people with dementia in Indonesia. Additional strategies are necessary to enhance longer-term adherence to the program.