Whole blood carbonic anhydrase activity (CAa) is increased in patients with obstructive sleep apnea (OSA). Our study investigated the influence of positive airway pressure (PAP) or CA inhibitor acetazolamide (ACT) therapy on CAa, OSA and blood pressure. Thirty‐three OSA patients (21 hypertensive, body mass index (BMI) 37 ± 7 kg/m2 and apnea–hypopnea index (AHI) of 47 ± 31 events/hr) were followed‐up after PAP treatment (compliance, 4.7 ± 1.5 hr/day; duration, median 6 [IQR 6,6] months) (Cohort A). A second OSA Cohort (B) contained nine hypertensive patients (BMI, 29 ± 4 kg/m2; AHI, 39 ± 20 events/hr) with 2‐week treatment of ACT, PAP or ACT + PAP in an open crossover study. CAa was assessed at baseline and at the end of each treatment period. In Cohort A, baseline CAa was higher in hypertensive, compared with normotensive, patients (1,033 ± 204 versus 861 ± 201 units, p = .028). PAP treatment reduced systolic/diastolic blood pressure but not CAa (−9 ± 11/−5 ± 7 mmHg and −20 ± 289 units, p < .001, <.001 and .70). In Cohort B, blood pressure was reduced in both ACT‐treated groups (−10 ± 10/−5 ± 7 mmHg, p = .043 and .019; and −5 ± 5/−13 ± 13 mmHg, p < .001 and .009). AHI was reduced in both groups: ACT only, −17 ± 9 events/hr p = .001; and ACT + PAP, −39 ± 19 events/hr, p < .001. PAP did not change CAa (p = .98) but activity tended to decrease after ACT with or without PAP (p = .081 and .056). CAa is elevated in hypertensive OSA patients. Long‐term PAP reduced blood pressure without affecting CAa. ACT reduced blood pressure and CAa. Increased CAa may constitute a physiological characteristic in OSA, contributing to comorbid hypertension.