Introduction Smartphone addiction has been associated with sleeping problems and psychological anxiety. However, little is known about the association of smartphone addiction, sleep quality and perceived stress amongst university students particularly in dentistry. This study investigated the association of these variables amongst dental students in a Jordanian dental faculty. Materials and methods A sample of 420 undergraduate dental students enrolled for academic year 2017/2018 at the Jordan University of Science and Technology participated in this study. They were given a set of self‐administered questionnaires which consisted of questions regarding demographic information, characteristics of smartphone use, assessment of smartphone addiction, sleep quality as well as perceived stress. Results The mean Smartphone Addiction Scale (SAS) score amongst Jordanian dental students was high (109.9 ± 23.8). The correlation between SAS and Global Pittsburg Sleep Quality Index (PSQI) score was significant (r = 0.137, P =0.005) indicating that the higher the smartphone addiction level, the poorer the quality of sleep. Similarly, a significant correlation was found between Perceived Stress Scale‐10 (PSS‐10) score and Global PSQI score (r = 0.348, P < 0.001) which implied that students who have higher perceived stress experienced poorer sleep quality. Year 3 students (clinical year), smartphone addiction and perceived stress were determinants of sleep quality. Conclusions Dental students who have high levels of smartphone addiction or high perceived stress levels experienced poor sleep quality. Identifying smartphone addicts amongst students as well as stressors are imperative measures to allow timely assistance and support in the form of educational campaigns, counselling, psychotherapy and stress management.