The outbreak of COVID-19 has been affecting the daily lives of almost everyone and puts huge psychological pressure on people worldwide, including Turkey. Anxiety and stress levels among university students were already a public health concern. Our study aims to demonstrate the anxiety and stress levels of university students in Turkey after the outbreak of COVID-19 according to the Coronavirus Anxiety Scale (CAS) and COVID Stress Scale (CSS). CAS is a brief mental health screener to identify probable cases of dysfunctional anxiety associated with the COVID-19 pandemic, and CSS was developed to understand and assess COVID-19-related distress. An online questionnaire was administered to active 1,265 university students in Turkey between February 27 and March 8, 2021, via Google forms. The questionnaire consists of three parts that assess participants' demographic information, anxiety, and stress levels related to the pandemic. According to CAS and CSS analysis, anxiety and stress levels were associated with each other and influenced university students during the COVID-19 pandemic. Both were associated with gender and family member loss. The academic year of students had a relationship with anxiety. It was observed that the danger factor was the highest stressor in university students in Turkey related to the novel coronavirus, followed by contamination fears. Both factors were shown as moderate stressors. As a result of the study, it was revealed that anxiety and stress associated with the COVID-19 pandemic are now included in the social, academic, and physical burdens of the university years, which are decisive and important in terms of mental development and psychological health of the person. It is essential to ascertain the long-term effects of COVID-19 and take effective precautions to support the physical and mental health of today's university students accordingly.