Background: Ischaemic heart disease, including myocardial infarction, is one of the main causes leading to heart failure as a consequence of ischaemic myocardial damage. In recent years, survival in the acute phase of myocardial infarction has improved significantly, but the high mortality rate within 12 months of hospital discharge (reaching up to 9.8% in Poland) remains a challenge. Therefore, the KOS-Zawał (MC-AMI) comprehensive 12-month post-MI care programme was introduced in Poland in 2017. Aim: This study aimed to assess body composition (including, but not limited to, the phase angle, visceral fat, total body fat, redistribution between intracellular and extracellular fluid in the body, and metabolic age) using a bioelectrical impedance analysis (BIA) in post-MI patients before and after early post-MI rehabilitation who were participating in the KOS-Zawał (MC-AMI) programme. Methods: This study involved an examination (before rehabilitation) of 94 post-myocardial infarction patients who were referred to a cardiology appointment within 7–10 days of hospital discharge, during which a clinical assessment, electrocardiogram, and biochemical blood tests (complete blood count, CRP, and serum creatinine) were performed. For various reasons (death, qualification for device implantation, non-completion of rehabilitation, failure to attend a follow-up BIA), data from 55 patients who were examined twice (before and after rehabilitation) were used for the final analysis. Measurements were taken using a high-grade Tanita MC-780 BIA body composition analyser, which measured the resistance of tissues to a low-intensity electrical impulse (not perceptible to the subject). Results: Participation in rehabilitation as part of the KOS-Zawał (MC-AMI) programme was associated with a decrease in metabolic age in patients, with a reduction in visceral fat levels and levels of adipose tissue in the lower and upper limbs. Moreover, a clinically beneficial reduction in the ratio of extracellular water to total body water was also observed. These changes were statistically significant (p < 0.005). In contrast, there were no statistically significant differences in the change in phase angle values in the subjects before and after the 5-week post-infarction rehabilitation. Conclusions: Participation in early post-myocardial infarction rehabilitation as part of the KOS-Zawał (MC-AMI) programme (25 training sessions) is associated with significant improvements in body composition parameters, such as visceral adipose tissue, limb fat, and water redistribution, and, consequently, a reduction in metabolic age, despite no significant increase in phase angle values. It was hypothesised that the good baseline condition of the subjects might explain the lack of significant change in the phase angle over the short observation period. For further analysis, it would be worthwhile to increase the number of patients with baseline reduced phase angle values and monitor changes in this parameter throughout rehabilitation and the entire MC-AMI programme, because changes in the phase angle may also be influenced by other programme components such as dietary or psychological education. It is worth considering implementing a regular BIA assessment in patients in the programme as a motivating stimulus for diligent exercise and extending rehabilitation to be followed by telerehabilitation or hybrid telerehabilitation.