Within the framework of digital sustainability, the increase in Internet consumption, and especially online social networks, offers social benefits, but is not without its drawbacks. For example, it can lead to psychological and/or psychiatric disorders in some people. Numerous researches are highlighting the similarities of these addictions with the consumption of toxic substances. University students are heavy users of the Internet and, in certain situations, addiction to online social networks can be the result of depression, harassment, and anxiety, among others, affecting their daily life, including their academic responsibilities. In recent months, an anomaly has occurred that may have contributed to intensifying this problem, namely the confinement produced by the COVID-19 pandemic, which has affected the whole world to a greater or lesser extent. In this cross-sectional study, with a descriptive and quantitative methodology, students from 14 Spanish universities were investigated in the first wave of the COVID-19 pandemic in order to understand the effects of this situation on the problem described. The results show a high consumption of social networks during that time, with significant incidences of addiction. In parallel, the presence of comorbidity has been determined. In this scenario, it would be necessary to implement university educational programs to redirect these addictive behaviors, as well as preventative recommendations and actions to minimize negative impacts. This is a major problem that is growing, exacerbated by the global pandemic produced by the SARS-CoV-2 coronavirus. Situations of this gravity call for the development of preventive and educational measures for the responsible and sustainable use of ICT.