For people with psoriasis, biomarkers aiding in the personalization of treatment with biologics are needed. We examined the usefulness of several biomarkers of inflammation in this respect. The neutrophil-to-lymphocyte ratio (NLR), the platelet-to-lymphocyte ratio (PLR), and the systemic immune–inflammation index (SII) were measured in patients with psoriasis initiating TNF-α inhibitors (n = 131), IL-17/IL-17R inhibitors (n = 65), or IL-23/IL-12/23 inhibitors (n = 50). The blood levels of tumor necrosis factor (TNF)-α, interleukin (IL)-1β, interferon (IFN)-γ, IL-17A, IL-6, soluble IL-6 receptor (sIL-6R), and soluble IL-6 signal transducer (sIL-6ST) were measured in patients initiating adalimumab (n = 62) or IL-17/IL-17R inhibitors (n = 24). Treatment response was defined by a psoriasis area and severity index (PASI) ≤ 2 three months after treatment initiation. Responders to TNF-α inhibitors had a lower NLR at baseline than non-responders (median and interquartile range (IQR) 2.15 (1.67–2.86) vs. 2.54 (1.88–3.55); p = 0.04). Responders to treatment with adalimumab had lower IL-6 levels at baseline than non-responders (0.99 (0.42–1.4) vs. 1.62 (0.96–2.41) pg/mL; p = 0.02). For the majority of patients, the IL-17A, IL-1β, and IFN-γ levels were below quantification limits. NLR and IL-6 may serve as predictive biomarkers of treatment response to TNF-α inhibitor therapy in patients with psoriasis.