Background/Objectives: Physical exercise (PE) has been shown to have positive effects on the symptoms associated with autism spectrum disorder (ASD). However, there is still no consensus on the most appropriate PE intervention model. With this in mind, we developed a program with the aim of determining the effects of PE on physical fitness, with a view to applying it as a potential treatment. Methods: Using an experimental methodology, this research work will recruit 18 institutionalized young people and adults who will be allocated to one of two groups, namely (i) the youth training group and (ii) the adult training group, using low-cost materials. Both intervention groups will perform 90 min of training per session, twice a week, for 12 weeks. Evaluations will be carried out at baseline and month 3. The impact of the exercise program will be assessed based on the variables of anthropometry, body composition, cardiovascular response, and cardiorespiratory fitness. Results: The results of this study will contribute to the development of more effective strategies, prescription recommendations, and interventions as a guarantee in future programs of better and greater adherence to PE by institutionalized individuals with ASD. Conclusions: In addition, we intend to make the PE program available if it promotes positive effects in the target population.