Oxidative stress and neuroinflammation are involved in the pathogenesis of alcohol addiction. However, little is known regarding the effect of genetic, behavioral, psychological, and environmental sources of origin on the inflammation and oxidative stress pathways of patients with alcohol addiction. Our study aimed to evaluate the impact of selected common functional single-nucleotide polymorphisms in inflammation and oxidative stress genes on alcohol addiction, and common comorbid psychosymptomatology. Our study included 89 hospitalized alcohol-addicted patients and 93 healthy individuals, all Slovenian males. Their DNA was isolated from peripheral blood and patients were genotyped for PON1 rs705379, rs705381, rs854560, and rs662, SOD2 rs4880, GPX1 rs1050450, IL1B rs1143623, rs16944, and rs1071676, IL6 rs1800795, IL6R rs2228145, and miR146a rs2910164. Kruskal–Wallis and Mann–Whitney tests were used for the additive and dominant genetic models, respectively. Our findings suggested the involvement of IL6 rs1800795 in alcohol addiction. Moreover, our data indicated that the genetic variability of SOD2 and PON1, as well as IL1B and IL6R, may be related to comorbid psychosymptomatology, revealing a potential indirect means of association of both the oxidative stress and inflammation pathways.