Background: Evidence suggests that non-aspirin non-steroidal anti-inflammatory drugs (NSAIDs) have antineoplastic properties of potential importance for survival of head and neck cancer. Methods: We conducted a nationwide cohort study including all individuals with primary head and neck squamous cell carcinoma in Denmark during 2000–2016 at age 30–84 years, with no history of cancer (except non-melanoma skin cancer), and alive at 1 year after diagnosis. Nationwide registries provided information on drug use, causes of death and potential confounders, and additional clinical information was obtained for a subpopulation. We conducted Cox proportional hazards regression to estimate multivariable-adjusted hazard ratios (HRs) with 95% confidence intervals (CIs) for the association between post-diagnosis non-aspirin NSAID use (defined as ≥1 filled prescription within first year after diagnosis) and cancer-specific mortality. Results: Among 10,770 head and neck cancer 1-year survivors, the HR for cancer-specific mortality with non-aspirin NSAID use was 1.68 at 1 year after diagnosis, but declined and stabilized around 1.15 (95% CI 1.02–1.29) at 2 years after diagnosis. Among 2-year survivors, the HRs for cancer-specific mortality with non-aspirin NSAID use remained slightly increased in analyses stratified by age, sex, stage, and pre-diagnosis non-aspirin NSAID use. Similar results were seen in the subpopulation (n = 1029) with additional clinical information, and among 5-year survivors with additional non-aspirin NSAID exposure assessment. Conclusion: In this nationwide cohort of patients with head and neck cancer, use of non-aspirin NSAIDs was associated with a slightly increased mortality risk, warranting further evaluation.