Diverse studies have shown that a significant percentage of the Spanish university population suffers from different addictions. They are both a personal and public health problem if there is not a greater awareness of the risks involved and if the appropriate prevention measures are not taken, among them educational ones. In this context, a descriptive and explanatory cross-sectional study was conducted during the first half of June 2020, coinciding with the period of confinement that occurred in Spain during the first wave of the COVID-19 pandemic. Given that this is such an exceptional time, the main objective of this study was to obtain information especially on students’ substance consumption and possible addictions at this time. Knowing the specific situation of this problem in that specific situation may allow for comparative studies in the future. The sample was composed of 310 university students from 14 Spanish universities. The instrument used in the research was the ASSIST questionnaire, developed by the WHO for the detection of alcohol, tobacco, and substance consumption. As result, a moderate and high risk was observed mainly in the following substances: alcohol (36.2%), tobacco (33.2%), cannabis (22.9%), and sedatives (10.3%). Through the logistic regression of the set of drugs, it has been proven that, on the one hand, the addiction to cocaine and sedatives in the family environment and age, on the other hand, are the main predictive variables of drug consumption. The existence of polysubstance abuse was also determined. These data show the need for educational bodies and university institutions to promote awareness, sensitization, and health education programs to deal with this important problem, especially in extraordinary situations, such as the one referred to, which could increase this consumption.