Background: Research regarding the feasibility and effects of dancing and exercise with musical support programmes on the physical fitness of adults with intellectual disability (ID) is scarce. The purpose of this study was to provide scientific evidence regarding the feasibility of a training programme consisting of dancing and exercise with music designed for adults with ID, as well as to assess its impact on their body composition and cardiovascular and muscular fitness. Methods: A total of 30 adults (mean age 36.37 ± 11.24 years) with mild (n = 13), moderate (n = 16) or severe (n = 1) ID took part in a 10-week dancing and exercise with music programme. Recruitment and completion rate, adherence to the programme, participation and adverse effects were registered as measures of feasibility. The body mass index, cardiovascular endurance (6-min walk test) and muscular strength (standing long jump test) of the participants were assessed in order to determine the effects of the programme on their fitness level. Results: A 92.5% recruitment rate and a 90% completion rate were achieved. Adherence to the programme stood at 76.6%, and no adverse effects were registered. The comparison between the values obtained in the initial and final evaluations indicated the existence of positive changes in all the fitness dimensions measured. Conclusion: A training programme combining dancing and exercise with music proved to be feasible when performed by adults with ID. These kind of programmes can have a positive effect on the fitness level of this specific group.