Smartphone use can lead to smartphone addiction, which is a growing concern worldwide. However, there are limited studies about smartphone addiction and its impacts on university students in Saudi Arabia. This study aims to fill this gap. This is a quantitative study conducted among undergraduate students in Umm Al-Qura University (UQU), Saudi Arabia from May 2019 and February 2021. Study data were collected using both online and hard copy administered surveys. A self-administered questionnaire, Grade point average, Smartphone Addiction Short Version, and Kessler Psychological Distress scales were used to assess the outcomes. A total of 545 undergraduate students, mostly females, aged ≤21 years old and lived with large family sizes. More than half owned a smartphone for 5–8 years and the majority used their smartphone on average 6–11 h per day for social networking (82.6%), entertainment (66.2%) and web surfing (59.6%). Most of the participants were smartphone-addicted (67.0%). Logistic regression analysis showed that age ≤ 21, not gainfully employed, small family size and high family income were the main significant socio-demographic predictors of smartphone addiction. Smartphone-addicted participants were more likely to: have lower academic performance (GPA); be physically inactive; have poor sleep; be overweight/obese; have pain in their shoulder (39.2%), eyes (62.2%) and neck (67.7%) and have a serious mental illness (30.7%). This finding has significant implications for decision makers and suggests that smartphone education focusing on the physical and mental health consequences of smartphone addiction among university students can be beneficial.