Psoriasis is an immune-mediated, chronic disorder that significantly alters patients’ quality of life and predisposes them to a higher risk of comorbidities, including liver fibrosis. Various non-invasive tests (NITs) have been validated to assess liver fibrosis severity, while blood-count-derived inflammatory markers have been proven to be reliable in reflecting inflammatory status in psoriatic disease. The fibrosis-4 (FIB-4) index became part of the newest guideline for monitoring psoriasis patients undergoing systemic treatment. Patients with psoriasis vulgaris and fulfilling inclusion criteria were enrolled in this study, aiming to assess for the first time in the literature whether such inflammatory markers are useful in predicting liver fibrosis. Based on internationally validated FIB-4 index values, patients were divided into two study groups: a low risk of significant fibrosis (LR-SF) and a high risk of significant fibrosis (HR-SF). Patients from HR-SF were significantly older and had higher values of the monocyte-to-lymphocyte ratio (MLR) (p < 0.001), which further significantly correlated with fibrosis severity (p < 0.001). Platelet-to-lymphocyte ratio (PLR), systemic immune inflammation index (SII), platelet-to-white blood cell ratio (PWR), and aggregate index of systemic inflammations (AISI) significantly correlated negatively with liver fibrosis (p < 0.001). PWR proved to be the most reliable inflammatory predictor of fibrosis severity (AUC = 0.657). MLR, PWR, and AISI were independent inflammatory markers in multivariate analysis (p < 0.001), while the AST to platelet ratio index (APRI) and AST to ALT ratio (AAR) can be used as additional NITs for significant liver fibrosis (p < 0.001). In limited-resources settings, blood-count-derived inflammatory markers such as MLR, PWR, and AISI, respectively, and hepatic indexes APRI and AAR prove to be of particular help in predicting significant liver fibrosis.