Background Antidepressant use has been associated with an increased risk of falling, but no studies have been conducted on whether antidepressant use is associated with an increased risk of head injuries which often result from falling among older persons. The objective of this study was to investigate the risk of head and brain injuries associated with antidepressant use among community-dwelling persons with Alzheimer’s disease. Methods A matched cohort study was conducted by comparing new antidepressant users (n = 10,910) with two matched nonusers (n = 21,820) in the MEDALZ study cohort. The MEDALZ cohort includes all community-dwelling persons newly diagnosed with Alzheimer’s disease between 2005 and 2011 in Finland. Incident antidepressant users were identified based on register-based dispensing data from the Prescription register with a 1-year washout period for antidepressant use. Nonusers were matched with users based on age, gender, and time since Alzheimer’s disease diagnosis. The outcome events were defined as any head injuries and traumatic brain injuries based on diagnoses in Hospital Discharge and Causes of Death registers. Propensity score adjusted Cox proportional hazard models were utilized. Sensitivity analyses with case-crossover design were conducted. All registers are linkable with unique personal identification numbers assigned for each resident. Results Antidepressant use was associated with an increased risk of head injuries (age-adjusted event rate per 100 person-years 2.98 (95% confidence interval (CI) 2.49–3.06) during use and 2.43 (95% CI 2.06–2.35) during nonuse, adjusted hazard ratio (HR) 1.35, 95% CI 1.20–1.52) and traumatic brain injuries (age-adjusted event rate per 100 person-years 1.33 (95% CI 1.13–1.53) during use and 1.10 (95% CI 1.00–1.20) during nonuse, adjusted HR 1.26, 95% CI 1.06–1.50). The risk was highest during the first 30 days of use (HR 1.71, 95% CI 1.10–2.66 for head injuries; HR 2.06, 95% CI 1.12–3.82 for traumatic brain injuries) and remained at an elevated level for head injuries for over 2 years of use. In case-crossover analyses, antidepressant use was consistently associated with a higher risk of head injuries. Conclusions Antidepressant use was associated with an increased risk of the most severe outcomes, head and brain injuries, in persons with Alzheimer’s disease. Antidepressant use should be carefully considered and the association confirmed in future studies. Electronic supplementary material The online version of this article (doi:10.1186/s13195-017-0285-3) contains supplementary material, which is available to authorized users.