Psoriasis is a chronic inflammatory disease that affects around 2–3% of the world’s population. The treatment for this autoimmune disease still remains centered around conventional methods using synthetic substances, even though more recent advancements focus on biological therapies. Given the numerous side effects of such treatments, current research involves plant extracts and constituents that could prove useful in treating psoriasis. The aim of this narrative review is to highlight the most known representatives belonging to classes of natural compounds such as polyphenols (e.g., astilbin, curcumin, hesperidin, luteolin, proanthocyanidins, and resveratrol), alkaloids (e.g., berberine, capsaicin, and colchicine), coumarins (psoralen and 8-methoxypsoralen), and terpenoids (e.g., celastrol, centelloids, and ursolic acid), along with plants used in traditional medicine that could present therapeutic potential in psoriasis. The paper also provides an overview of these compounds’ mechanisms of action and current inclusion in clinical studies, as well as an investigation into their potential incorporation in various nanotechnological systems, such as lipid-based nanocarriers or polymeric nanomaterials, that may optimize their efficacy during treatment.