(1) Background: COVID-19 has had psychological impacts, particularly anxiety, depression, anger, and suicidal ideation, on the world’s populace, including young persons who were prone to mental health disorders even before the pandemic. We described the psychological impacts of COVID-19 among emerging adults aged 18–30 years in Saudi Arabia. (2) Methods: A cross-sectional survey was done among a randomly sampled population in Saudi Arabia between July 2020 and May 2021 using the DSM-5 Self-rated Level 1 Cross-Cutting Symptom Measure and Ask Suicide Questionnaire. Logistic regression was used to assess participant characteristics associated with reporting symptoms of mental disorders under each of the 13 domains that would warrant further investigation. (3) Results: Approximately, 91% of participants experienced different mental health symptoms; these participants are more likely to be young, female students, those who had a history of being diagnosed with a mental disorder, and those diagnosed or treated for COVID-19. (4) Conclusion: This study strongly showed an increased prevalence of mental health symptoms among young persons during the COVID-19 pandemic. Addressing the mental health burden among young persons in time using simple, self-administered screening tools linked to interventions will prevent dire consequences in the future.