The combination of exercise and nutritional intervention is widely used for stroke patients, as well as frail or sarcopenic older persons. As previously shown, supplemental branched chain amino acids (BCAAs) or protein to gain muscle mass has usually been given just after exercise. This study investigated the effect of the timing of supplemental BCAAs with exercise intervention on physical function in stroke patients. The participants were randomly assigned to two groups based on the timing of supplementation: breakfast (n = 23) and post-exercise (n = 23). The supplement in the breakfast group was provided at 08:00 with breakfast, and in the post-exercise group it was provided just after the exercise session in the afternoon at 14:00–18:00. In both groups, the exercise intervention was performed with two sessions a day for two months. The main effects were observed in body fat mass (p = 0.02, confidence interval (CI): 13.2–17.7), leg press strength (p = 0.04, CI: 94.5–124.5), and Berg balance scale (p = 0.03, CI: 41.6–52.6), but no interaction with intake timing was observed. Although the effect of the timing of supplementation on skeletal muscle mass was similar in both groups, BCAA intake with breakfast was effective for improving physical performance and decreasing body fat mass. The results suggest that a combination of BCAA intake with breakfast and an exercise program was effective for promoting rehabilitation of post-stroke patients.