The first case of infection by SARS-CoV-2 (i.e., COVID-19) was officially recorded by the Italian National Health Service on 21 February 2020. Respiratory tract manifestations are the most common symptoms, such as gastrointestinal symptoms (GISs) like nausea or sickness, diarrhea, and anorexia, and psychological effects may be reported in affected individuals. However, similar symptoms may be observed in healthy people as a consequence of an anxiety state. Methods: We analyzed GISs and anxiety state during the COVID-19 lockdown period; from 9 March 2020 to 4 May 2020. A web-based survey consisting of 131 items was administered to 354 students affiliated with the School of Medicine of the University “Magna Graecia” of Catanzaro; Italy. A set of statistical analyses was performed to analyze the relationships among the answers to assess a correlation between the topics of interest. Results: The statistical analysis showed that 54.0% of interviewed reported at least one GISs, 36.16% of which reported a positive history for familial GISs (FGISs). The 354 subjects included in our cohort may be stratified as follows: 25.99% GISs and FGISs, 27.97% GISs and no-FGISs, 10.17% no-GISs and FGISs, 35.87% no-GISs and no-FGISs. Results indicated an anxiety state for 48.9% of respondents, of which 64.74% also presented GISs. In addition, considered dietary habits, we detect the increased consumption of hypercaloric food, sweetened drinks, and alcoholic beverages. Conclusions: The increase of GISs during the lockdown period in a population of medical students, may be correlated to both dietary habits and anxiety state due to a concern for one’s health.