Background: Increasing smartphone use has led to the introduction of smartphone addiction as a behavioral addiction with detrimental effects on health. This phenomenon has not been widely studied in the Indian context. This study assessed the rate of smartphone addiction in a sample of medical students, with a focus on its correlation with sleep quality and stress levels. Methods: A cross-sectional study was conducted between November 2016 and January 2017 in 195 medical students. Their smartphone use, level of smartphone addiction, sleep quality, and perceived stress levels were measured using the Smartphone Addiction Scale-Short Version (SAS-SV), the Pittsburgh Sleep Quality Index (PSQI), and the Perceived Stress Scale (PSS-10), respectively. Results: Of the 195 students, 90 (46.15%) had smartphone addiction as per the scale. A self-reported feeling of having smartphone addiction, use of the smartphone right before sleeping, PSS scores, and PSQI scores were found to be significantly associated with the SAS-SV scores. Significant positive correlations were observed between the SAS-SV and PSS-10 scores, and the SAS-SV and PSQI scores. Conclusions: There is a high magnitude of smartphone addiction in medical students of a college in Western Maharashtra. The significant association of this addiction with poorer sleep quality and higher perceived stress is a cause for concern. The high self-awareness among students about having smartphone addiction is promising. However, further studies are required to determine whether this self-awareness leads to treatment seeking. Further studies are required to explore our finding of the association of smartphone addiction with using the smartphone before sleeping.