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Previous observational studies reported associations between non-steroidal anti-inflammatory drugs (NSAIDs) and major depressive disorder (MDD), however, these associations are often inconsistent and underlying biological mechanisms are still poorly understood. We conducted a two-sample Mendelian randomisation (MR) study to examine relationships between genetic variants and NSAID target gene expression or DNA methylation (DNAm) using publicly available expression, methylation quantitative trait loci (eQTL or mQTL) data and genetic variant-disease associations from genome-wide association studies (GWAS of MDD). We also assessed drug exposure using gene expression and DNAm levels of NSAID targets as proxies. Genetic variants were robustly adjusted for multiple comparisons related to gene expression, DNAm was used as MR instrumental variables and GWAS statistics of MDD as the outcome. A 1-standard deviation (SD) lower expression of NEU1 in blood was related to lower C-reactive protein (CRP) levels of −0.215 mg/L (95% confidence interval (CI): 0.128–0.426) and a decreased risk of MDD (odds ratio [OR] = 0.806; 95% CI: 0.735–0.885; p = 5.36 × 10−6). A concordant direction of association was also observed for NEU1 DNAm levels in blood and a risk of MDD (OR = 0.886; 95% CI: 0.836–0.939; p = 4.71 × 10−5). Further, the genetic variants associated with MDD were mediated by NEU1 expression via DNAm (β = −0.519; 95% CI: −0.717 to −0.320256; p = 3.16 × 10−7). We did not observe causal relationships between inflammatory genetic marker estimations and MDD risk. Yet, we identified a concordant association of NEU1 messenger RNA and an adverse direction of association of higher NEU1 DNAm with MDD risk. These results warrant increased pharmacovigilance and further in vivo or in vitro studies to investigate NEU1 inhibitors or supplements for MDD.