Herpesviruses are DNA viruses that infect humans and animals with the ability to induce latent and lytic infections in their hosts, causing critical health complications. The enrolment of nutraceutical anti-herpesvirus drugs in clinical investigations with promising levels of reduced resistance, free or minimal cellular toxicity, and diverse mechanisms of action might be an effective way to defeat challenges that hurdle the progress of anti-herpesvirus drug development, including the problems with drug resistance and recurrent infections. Therefore, in this review, we aim to hunt down all investigations that feature the curative properties of curcumin, a principal bioactive phenolic compound of the spice turmeric, in regard to various human and animal herpesvirus infections and inflammation connected with these diseases. Curcumin was explored with potent antiherpetic actions against herpes simplex virus type 1 and type 2, human cytomegalovirus, Kaposi’s sarcoma-associated herpesvirus, Epstein–Barr virus, bovine herpesvirus 1, and pseudorabies virus. The mechanisms and pathways by which curcumin inhibits anti-herpesvirus activities by targeting multiple steps in herpesvirus life/infectious cycle are emphasized. Improved strategies to overcome bioavailability challenges that limit its use in clinical practice, along with approaches and new directions to enhance the anti-herpesvirus efficacy of this compound, are also reviewed. According to the reviewed studies, this paper presents curcumin as a promising natural drug for the prevention and treatment of herpesvirus infections and their associated inflammatory diseases.