Background: This study is a quantitative analysis examining the impact of the COVID-19 pandemic on the occurrence of stress and stomatognathic system disorders (SSDs) among students of physiotherapy. Objective: To assess stress severity, strategies of coping with stress and the presence of type D personality among physiotherapy students including those with symptoms of stomatognathic system disorders. Material and Methods: The research was conducted from October to December 2020 on a sample of 188 students of physiotherapy. The data were collected using a survey form related to the occurrence of SS disorders symptoms and standardized psychological questionnaires, such as the Perceived Stress Scale (PSS)- 10, Mini-Cope, and the type-D Scale (DS14), developed for the purpose of this study. Results: Women experiencing at least one of the SS disorder-related symptoms were characterized by a significantly higher level of stress and a type D personality (p < 0.05). Among men, these differences were not statistically significant (p > 0.05). On the basis of the strategies of coping with stress, i.e., positive self-reevaluation, discharging and blaming oneself, and taking psychoactive substances, it is possible to predict the intensity of stress during the pandemic in the group of the examined students. Among the reported symptoms of SS, headache was a significant predictor of stress, which was accompanied by an increase in the intensity of stress by nearly 0.2 measurement points. Students with higher levels of stress showed more symptoms of type D personality, and those with more severe symptoms of SS showed higher levels of stress. Conclusions: People prone to stress and having type D personality traits should be assessed for the presence of SS disorders.