Background: Dementia involves the loss of cognitive abilities and represents a decline from the prior level of function, which impairs functional abilities in day-to-day life. The purpose of the present study is to examine the effectiveness of an exercise program on the muscle strength and range of motion of the upper limbs, the functional status, and the depression of elderly people with early stage dementia. Methods: The sample consisted of 60 elderly people with early stage dementia who were randomly divided into a control and an experimental group of 30 participants each. The experimental group received a 12-week Otago exercise program with 45 min duration of each session. The control group received usual care without doing exercise. The outcome measures of muscle strength and range of motion of the upper limbs, the functional status, and the depression were assessed by valid instruments and tests at the beginning and at the end of the intervention program. Repeated measures one-way ANOVA and Mann-Whitney tests examined the differences between the two groups at the end of the 12-week exercise program. Results: Statistically significant differences were found between the experimental and control groups in the entire outcome measures (functional ability F = 9.35 p < 0.05; muscle strength right hand F = 32.33, p < 0.05 left hand U = 95.50 p < 0.01; e.g., range of motion shoulder extension U = 104.00 p < 0.01), except depression. Conclusions: Both muscle strength and range of motion of the upper limbs, as well as the functional ability, were improved by the exercise program. Further research is needed to investigate the present results, in particular to explore the long-term cognitive, behavioral, and functional status outcomes of exercise in the early stages of dementia.