Background: Hepatitis C virus (HCV) management is a challenge in patients with substance use disorder (SUD). This study aimed to describe an HCV screening and linkage to care program in SUD patients, and analyze the characteristics of this population in relation to HCV infection, particularly the impact of psychiatric comorbidities (dual diagnosis). Methods: This study was a prospective clinical cohort study using a collaborative, multidisciplinary model to offer HCV care (screening, diagnosis, and therapy) to individuals with SUD attending a dedicated hospital clinic. The characteristics of the participants, prevalence of HCV infection, percentage who started therapy, and adherence to treatment were compared according to the patients’ consumption characteristics and presence of dual diagnosis. HCV screening, diagnosis, treatment initiation, and sustained virologic response were analyzed. Results: 528 individuals attended the center (November 2018–June 2019) and 401 (76%) accepted screening. In total, 112 (28%) were anti-HCV-positive and 42 (10%) had detectable HCV RNA, but only 20 of the latter started HCV therapy. Among the 253 (63%) patients with a dual diagnosis, there were no differences in HCV infection prevalence versus patients with SUD alone ( p = 0.28). Dual diagnosis did not lead to a higher risk of HCV infection or interfere with linkage to care or treatment. Conclusion: This study found a high prevalence of dual diagnosis and HCV infection in SUD patients, but dual diagnosis was not associated with an increased risk of acquiring HCV or more complex access to care. Despite use of a multidisciplinary management approach, considerable barriers to HCV care remain in this population that would need more specific focus.