Background: Patients with psoriasis often experience psychiatric comorbidities, such as depression and anxiety. These comorbidities can lead to poorer adherence to treatment regimens, reduced effectiveness of therapies, and a heightened disease burden. This study aims to explore the scientific output related to psoriasis, depression, and anxiety using a comprehensive analysis combining bibliometric statistical methods. Methods: The study performed a bibliometric analysis of publications related to psoriasis, depression, and anxiety between 1974 and December 2023. This study employed the Latent Dirichlet Allocation (LDA) algorithm to identify key research topics and used the HJ-Biplot technique to visualize the relationships between publications and research indicators. The inclusion criteria were limited to English-language research articles. Results: Over 49 years, the analysis identified 5059 documents published across 1151 sources. The annual growth rate for research was 12.26%. The Journal of the European Academy of Dermatology and Venereology and The British Journal of Dermatology were found to be the leading journals in this field. The United States emerged as the top contributor, followed by China, Italy, and Germany. The most prevalent research topics were inflammation and cellular function, with a significant focus on patient treatment and the impact of depression and anxiety. Conclusions: This bibliometric analysis underscores the increasing of studies on the comorbidities of depression and anxiety in patients with psoriasis. This study provides a comprehensive overview of research trends and emerging topics in this field, offering valuable insights for future investigations.