Introduction: Academic and emotional challenges faced by medical students can affect their psychological well-being and health. Personal characteristics may also predispose one to the manifestation of distress reactions. Individuals with type D personality have an increased tendency to develop depressive reactions and somatic diseases, including the presence of cognitive dysfunction. In students, the presence of cognitive dysfunction may additionally adversely affect academic and psycho-emotional problems. The purpose of this study was to examine the influence of type D personality and coping strategies on cognitive functioning in medical students. Methods: A cross-sectional study included 258 medical students (age 19 ± 1.2 years, 79 men). All participants completed psychological questionnaires (DS-14 to identify type D personality, and The Coping Strategy Indication, CSI—to determine coping strategies), as well as extensive neuropsychological testing of cognitive functions. Results: Among the medical students examined, the frequency of identification of type D personality was 44%. In persons with personality type D, according to psychometric testing, a decrease in the level of functional mobility of nervous processes (FMNP) was noted, which was manifested in an increase in the test completion time (p < 0.001) and an increase in the number of errors (p < 0.001) during the FMNP test, and an increase in the test completion time in the attention concentration test. In addition, in type D participants, an increase in the test execution time during the attention test was noted (p = 0.007). Personality type D was an independent risk factor for cognitive decline in students in multiple linear regression analysis, when type D was analyzed as a dichotomous construct. Conclusions: Assessing personal characteristics and identifying personality type D is advisable for medical students, to develop subsequent programs to increase their resistance to academic challenges, improve cognitive function, and also to prepare for future stress loads during professional activities in the field of healthcare.