Since 25 March 2020, all schools, colleges, and universities in Poland have indefinitely closed and, where possible, have activated distance learning because of the COVID-19 pandemic. Considering that the undergraduate years are usually characterized by a high prevalence of emotional disorders and sleep problems, it can be expected that the current situation may have a remarkable impact on the student population. This study aimed to investigate the occurrence of sleep problems among Polish university students as well as the relationship of insomnia symptoms severity with psychopathological symptoms, posttraumatic stress disorder (PTSD) symptoms, and behavioral factors, such as substance use, changes in the amount of sleep, and the level of physical activity during the COVID-19 pandemic. Data were collected from 1111 Polish university students via an online survey conducted between IV and VI 2020. The survey included demographic variables, the level of psychopathological symptoms (General Health Questionnaire, GHQ-28), insomnia (Insomnia Severity Index, ISI), and symptoms of posttraumatic stress (Impact of Events Scale-Revised, IES-R). The results showed that over half of the studied group of students had some form of sleep disturbances during the period of data collection, with moderate-to-severe insomnia symptoms noted in 21.6%. At the same time, the majority of the sample declared they slept more during the pandemic. A significant positive correlation was observed between the severity of insomnia symptoms and PTSD symptoms, as well as GHQ scores, increased substance use, and decreased physical activity. An additional association between the presence of dreams related to the event and insomnia symptoms as well as GHQ scores has been found. The results suggest that sleep problems may be prevalent among university students during the pandemic. Moreover, although the symptoms of insomnia, as well as the severity of sleep disturbance, significantly correlated with all the investigated variables, the direction of those associations remains to be established.