Multiple sclerosis subjects treated with natalizumab face anxiety about developing progressive multifocal leukoencephalopathy (PML), besides the psychological distress caused by the disease. The aim of this study is to investigate whether increasing the frequency of neurological and nuclear magnetic resonance screening may affect anxiety and the perception of disease control in patients treated with natalizumab. A total of 62 relapsing–remitting multiple sclerosis patients were recruited from 2019 to 2020. All patients received conventional infusion treatments with natalizumab, along with a screening protocol for PML. Three clinical assessments were considered: at the beginning of the study (T0), after 3 months (T1) and after 6 months (T2). Patients were classified into three levels of risk, where level 1 represented a low risk of PML and level 3 a high risk. This classification determined treatment and screening protocol, i.e., the frequency of performing the Stratify test and the brain 3T NMR exam, as well as the frequency of infusion treatments. Anxiety and perception of disease control were assessed at T0, T1, and T2 by a skilled psychologist. The Friedman test and the Wilcoxon signed-rank test were used to compare outcomes at baseline with the two follow-ups. Statistical test results showed that the risk of PML (per 1000 patients) was significantly lower in women than in men (W = 198.5; p = 0.01). Moreover, significant differences between baseline and the two follow-ups were found, both for anxiety (F(2) = 122.6, p < 0.001) and for perception of disease control (F(2) = 123.5, p < 0.001). In both cases, there was significant improvement between baseline (T0) and the end of the study (T2) in any risk level (p < 0.001). An increase in the number of follow-ups, as well as an increase in instrumental investigations, might have a positive effect on both anxiety and the perception of disease control. However, there are many variables involved in the disease process that have an impact on patients’ psychological well-being. Therefore, further and more extensive studies are necessary to evaluate how, and how much, each variable impacts the disease course.