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Background: Coronary artery disease (CAD) is a chronic inflammatory disorder characterized by atherosclerotic plaque formation and progression. Identifying reliable, inexpensive biomarkers to predict its presence and severity remains clinically important. This study aimed to evaluate the role of the neutrophil-to-albumin ratio (NAR), a novel inflammatory index, in predicting CAD and its severity. Methods: A total of 987 patients who underwent coronary angiography (CAG) due to suspected CAD were retrospectively analyzed. The severity of coronary atherosclerosis was quantified using the Gensini score. Patients were divided into three groups: normal (score 0), mild (1–24), and severe (≥25). NAR was calculated by dividing the neutrophil count by serum albumin concentration. Statistical analyses included ANOVA, receiver operating characteristic (ROC) analysis, and multivariate ordinal logistic regression. Results: Higher NAR levels were significantly associated with increased Gensini scores (p < 0.001). ROC analysis identified an optimal NAR cut-off value of 0.1138 for predicting CAD severity (AUC = 0.735, p < 0.001). In the multivariate model, NAR remained the strongest independent predictor of ischemia severity (OR 1.82, 95% CI 1.48–2.24, p < 0.001), followed by diabetes mellitus and hypertension. Conclusions: NAR is an easily obtainable, inexpensive, and independent biomarker that may predict both the presence and severity of CAD. These findings suggest that NAR could be a practical parameter for early risk stratification before invasive coronary evaluation.