Many clinical practice recommendations indicate rehabilitation as essential for patients with sequelae of severe or critical COVID-19 and suggest the prompt initiation of a multicomponent rehabilitation program focused on aerobic and endurance training. However, randomized controlled trials (RCTs) regarding aerobic exercise are lacking. Therefore, we aimed to assess the feasibility and effectiveness of the addition of aerobic training to standard rehabilitation in subjects with subacute COVID-19. Participants were 32/214 patients with the sequelae of severe or critical COVID-19 in the acute phase who were eligible and agreed to participate in the study (eligibility = 15%, recruitment = 100%). After randomization and assessment with functional and strength tests, all the participants underwent an inpatient-tailored rehabilitation program (50 min/day, 5 days/week, 10 sessions); in addition, the experimental group performed a low- to moderate-intensity aerobic exercise (30 min/day, 10 sessions). No dropouts or severe adverse events were reported, with an attendance rate of 95.6%. Most of the secondary outcomes significantly improved in both groups, but the improvement in the Functional Independence Measure and Cumulated Ambulation Score—Italian version was significantly greater in the experimental group (at least, p < 0.05). This RCT showed that aerobic exercise is feasible and safe in subacute COVID-19. Moreover, it appears to be beneficial and useful in improving patients’ independence and mobility.