The pandemic declared in many countries in 2020 due to COVID-19 led to the freezing of economies and the introduction of distance learning in both schools and universities. This unusual situation has affected the mental state of citizens, which has the potential to lead to the development of post-traumatic stress and depression. This study aimed to assess the level of stress in dental students in the context of the outbreak of the SARS-CoV-2 virus pandemic. A survey on the PSS-10 scale was prepared to measure the level of perceived stress. The study included 164 dental students at the Faculty of Medical Sciences of the Medical University of Silesia in Katowice, Poland. The results showed the impact of COVID-19 on the stress of students, with 67.7% reporting high levels of stress. The study also revealed that stress was higher among older female students. This paper recommends that the university provide more intensive psychological care as psychological first aid strategies in epidemics or natural disasters and to consider telemedicine in order to deliver services due to the limitations of the pandemic.