Purpose: During the coronavirus disease 2019 (COVID-19) pandemic quarantine, university students were under various types of stressors, including the exams period, which might have affected their quality and quantity of sleep, and consequently, their quality of life. This study aimed to investigate the pattern and predictors of nightmares among university students and coinvestigate the presence of other types of sleep disturbances, mental disorders, and quarantine-related stressors. Methods: This cross-sectional study included 368 university students who answered a self-completed questionnaire covering their sociodemographic features, nightmare indicators, and associated quarantine stressors. Additionally, sleep disturbances were measured using the Generalized Sleep Disturbance Scale (GSDS), anxiety using the Generalized Anxiety Disorder 2 scale, and depression using the Patient Health Questionnaire-2. Results: The participants’ mean age was 20.4 ± 1.6 years, and male participants represented 35.9% of the sample. Nightmares were experienced by 117 (31.8%) of the participants, of whom 44.4% had new-onset nightmares. The mean GSDS was 45.0 ± 14.9 (min. = 12, max. = 130). This value is associated with elevated odds of the following outcomes: the presence of nightmares (odds ratio [OR] = 1.8; confidence interval [CI] 95% = 1.1–3.0); new-onset nightmares at the time of pandemic (OR = 2.6; CI 95% = 1.3–5.5); and anxiety (OR = 1.74; CI 95% = 1.0–2.9). The presence of nightmares elevated the score of GSDS by 11.3 points (S.E. = 1.6, p < 0.001), elevated the odds of anxiety by 4.1 (CI 95% = 2.5–6.8), and depression by 2.1 (CI 95% = 1.3–3.4). Conclusions: Stressors resulting from both the exams period and the fact that it was conducted during COVID-19 quarantine increased the rate and affected the pattern of nightmares. These stressors also led to other sleep disturbances and mental disorders that were significantly more prevalent among females.