Adherence is important for an exercise program’s efficacy. This study aims at investigating whether the COVID-19 lockdown had different consequences on the adherence to an exercise program specifically designed for women with postmenopausal osteoporosis when administered as individual home training (IHT) or gym group training (GGT). At the start of the lockdown, which imposed the temporary closure of any gym activities, GGT participants were invited to continue to exercise at home. IHT participants continued to exercise at home as usual. Adherence was recorded via logs and measured as the percentage of exercise sessions actually performed out of the total number of scheduled sessions in three 1-month periods: one before (PRE) and two after (M1 and M2) the beginning of lockdown. Before lockdown, IHT (66.8% ± 26.6) and GGT (76.3% ± 26.6) adherence were similar. During lockdown, IHT participation increased (M1: 81.5% ± 31.0; M2: 88.0% ± 28.3), while that of GGT showed no statistical differences (M1: 79.4% ± 34.2; M2: 80.6% ± 36.4). Exercise protocols based on supervised gym practice must consider the possibility of disruptive events, which could cause a sudden interruption of gym activity and include educational initiatives to instruct participants to exercise effectively and safely without a trainer’s direct supervision.