(1) Background: During the COVID-19 pandemic, strict lock-down and quarantine were widely imposed by most governments to minimize the spread of the virus. Previous studies have investigated the consequences of the quarantine and social isolation on mental health and the present study examines loneliness and problematic internet use. (2) Methods: The current research used a cross-sectional survey during a lock-down phase of the COVID-19 pandemic. A sample of 593 participants from the Middle East region (Kuwait, Saudi Arabia) were tested using the short form of the Revised UCLA Loneliness Scale and the Internet Addiction Test. (3) Results: Results from regression analyses showed an association between loneliness and Problematic Internet Use (PIU), and an association between loneliness and the number of hours spent online. Younger participants reported greater loneliness. The quality of the relationship with the person(s) with whom they were spending their lock-down was also correlated with loneliness. Those who reported greater loneliness also obtained frequent news about the pandemic from social media. Problematic internet use was associated with loneliness and the predictors of loneliness. ANOVA analyses showed a dose-response between the predictors and PIU. (4) Conclusions: This study highlights the influence of the social characteristics of the local culture during the COVID-19 lock-down on feelings of loneliness and on PIU.