(1) Background: limited data exist regarding the occurrence of hypotension associated with dexmedetomidine use and its risk factors in the context of intraoperative sedation for patients receiving peripheral nerve blocks. (2) Method: This single-center retrospective study assessed the incidence of hypotension in patients undergoing orthopedic upper extremity surgery with brachial plexus blockade. Patients were classified into three groups: group N (non-sedated), group M (midazolam), and group D (dexmedetomidine), based on their primary intraoperative sedative use. The primary outcome was the incidence of perioperative hypotension, defined as systolic blood pressure (SBP) < 90 mmHg or mean blood pressure (MBP) < 60 mmHg, at a minimum of two recorded time points during the intraoperative period and post-anesthesia care unit stay. Multivariable logistic models for the occurrence of hypotension were constructed for the entire cohort and group D. (3) Results: A total of 2152 cases (group N = 445, group M = 678, group D = 1029) were included in the analysis. The odds ratio for the occurrence of hypotension in group D was 5.68 (95% CI, 2.86 to 11.28) compared with group N. Concurrent use of a beta blocker, longer duration of surgery, and lower preoperative SBP and higher preoperative heart rate were identified as significant risk factors. (4) Conclusions: the increased risk of hypotension and the associated factors should be taken into account before using dexmedetomidine in these cases.