The aims of the study were to evaluate the responsiveness of Hospital Anxiety and Depression Scale-Anxiety (HADS-A) subscale and HADS-Depression (HADS-D) subscale to pulmonary rehabilitation (PR) in patients with bronchiectasis compared to a matched group of patients with chronic obstructive pulmonary disease (COPD) and provide estimates of the minimal clinically important difference (MCID) of HADS-A and HADS-D in bronchiectasis. Patients with bronchiectasis and at least mild anxiety or depression (HADS-A ≥ 8 or/and HADS-D ≥ 8), as well as a propensity score-matched control group of patients with COPD, underwent an 8-week outpatient PR programme (two supervised sessions per week). Within- and between-group changes were calculated in response to PR. Anchor- and distribution-based methods were used to estimate the MCID. HADS-A and HADS-D improved in response to PR in both patients with bronchiectasis and those with COPD (median (25th, 75th centile)/mean (95% confidence interval) change: HADS-A change: bronchiectasis −2 (−5, 0), COPD −2 (−4, 0); p = 0.43 and HADS-D change: bronchiectasis −2 (−2 to −1), COPD −2 (−3 to −2); p = 0.16). Using 26 estimates, the MCID for HADS-A and HADS-D was −2 points. HADS-A and HADS-D are responsive to PR in patients with bronchiectasis and symptoms of mood disorder, with an MCID estimate of −2 points.