The aim was to assess perceived stress (PS) and factors associated with PS in Russian medical and dental students. A total of 406 medical and 283 dental students aged 18–25 years that attended the Northern State Medical University in Arkhangelsk, North-West Russia participated in this cross-sectional study. A structured, self-administered questionnaire was used to collect information on socio-demographic and socioeconomic factors, oral health (OH) behavior, and self-reported OH. All students were clinically examined to assess dental caries, oral hygiene, and gingiva. PS was measured by the Perceived Stress Scale 10 (PSS-10). Of the students, 26.0%, 69.1%, and 4.9% reported low, moderate, and high PS, respectively. Female sex (b = 2.28, 95% confidence interval (CI): 1.38–3.18), dental faculty (b = 1.74, 95% CI: 0.94–2.54), low subjective socioeconomic status (SES) (b = 1.71, 95% CI: 0.91–2.51), and irregular dental visits (b = 1.65, 95% CI: 0.72–2.58) were associated with higher PSS-10 score. These factors were assumed to be clinical meaningful, given that minimal clinically important difference of PSS-10 fell between 2.19 and 2.66 points. The majority of the medical and dental students reported moderate PS. Based on statistical significance and clinical meaningfulness, socio-demographic factors (sex, faculty), subjective SES, and OH behavior (regularity of dental visits) were associated with PS.