Postoperative neurological deficits remain a concern for patients undergoing cardiac surgeries. Even minor injuries can lead to neurocognitive decline (i.e., postoperative cognitive dysfunction). Dexmedetomidine may be beneficial given its reported neuroprotective effect. We aimed to investigate the effects of dexmedetomidine on brain injury during cardiac surgery anaesthesia. This prospective observational study analysed data for 46 patients who underwent coronary artery bypass graft surgery with extracorporeal circulation between August 2018 and March 2019. The patients were divided into two groups: control (CON) with typical anaesthesia and dexmedetomidine (DEX) with dexmedetomidine infusion. Concentrations of the biomarkers matrix metalloproteinase-12 (MMP-12) and myelin basic protein (MBP) were measured preoperatively and at 24 and 72 h postoperatively. Cognitive evaluations were performed preoperatively, at discharge, and 3 months after discharge using Addenbrooke’s Cognitive Examination version III (ACE-III). The primary endpoint was the ACE-III score at discharge. Increased MMP-12 and MBP concentrations were observed in the DEX group 24 and 72 h postoperatively. No significant differences in ACE-III scores were observed between the groups at discharge; however, the values were increased when compared with initial values after 3 months (p = 0.000). The current results indicate that the administration of dexmedetomidine as an adjuvant to anaesthesia can increase MMP-12 and MBP levels without effects on neurocognitive outcomes at discharge and 3 months postoperatively.