Nowadays, the use of social networks (SNs) is pervasive and ubiquitous. Among other things, SNs have become a key resource for establishing and maintaining personal relationships, as further demonstrated by the emergence of the pandemic. However, easy access to SNs may be a source of addictive behaviour, especially among the younger population. The literature highlights various psychological and physiological factors as possible predictors of vulnerability to SN addiction. This paper explores the joint effects of stress level and cognitive absorption, in the form of temporal dissociation while on SNs, on the addiction of university students to SNs. Here, 312 participants were involved in an online survey. About 14% of the sample presented a risk for SN addiction. Moreover, it was found that stress level predicted SN addiction both directly and indirectly through the effect of individual temporal dissociation, as experienced during SN usage. These results suggest a significant role of perceived stress level on addiction risk, while also pointing out additional vulnerability to SN addiction for cognitive profiles that are relatively more prone to temporal dissociation while online.