The presence of psychological distress has a negative impact not only on cancer patients’ quality of life but also on the course of the disease, with slower recovery and increased morbidity. These issues are of particular importance in melanoma patients (MP), who remain at risk of disease progression for many years after diagnosis. This study aimed to investigate psychological distress, coping strategies, and their possible relationships with demographic–clinical features in patients with early-stage melanoma in follow-up. The investigation focused in particular on whether the psychological profile differed between patients at different melanoma stages. Data of 118 patients with melanoma in the Tis-Ia stages (MP_Tis-Ia) and 86 patients with melanoma in the Ib–IIa–IIb stages (MP_Ib–II) were gathered through a self-administered survey and compared using a cross-sectional design. The results evidenced a high percentage of anxiety (25%) and distress symptoms (44%), whereas depressive symptoms seemed less frequent (8%). Psychological distress was higher in women than in men, and in patients with a higher educational level. Nevertheless, no significant differences were found between MP_Tis-Ia and MP_Ib–II. With respect to coping style, the patients in this sample adopted predominantly positive and active strategies. Correlational analyses showed that maladaptive coping strategies such as behavioral disengagement, denial, self-distraction, and self-blame were most strongly related to increased levels of psychological distress. The high presence of anxiety and distress symptoms, their relationship, and the use of negative coping strategies underline the importance of psychological distress screening also in early-stage MP, including at long-term follow-up.