Due to the COVID-19 pandemic, educational institutions globally were forced to close, resulting in a transition to online learning. However, this transition increased screen time and made e-learners more vulnerable to biopsychosocial issues. This study aimed to assess the impact of online learning on the eyes and mental health of medical science students, including those pursuing MBBS, Nursing, Optometry, Pharmacy, and Veterinary degrees during the COVID-19 lockdown period. A cross-sectional quantitative study was conducted, collecting online data from 182 samples using a socio-demographic data sheet (SDVS), Computer Vision Symptom Scale (CVSS 17), and the Perceived Stress Scale (PSS 10). Results revealed that most students spent between 2 and 4 h and >7 h on electronic devices before and during COVID-19, respectively, with many reporting moderate mental stress and eye strain. A weak positive correlation (r = 0.204 at p < 0.05) was found between perceived stress and eye strain, with the 24–29 age group reporting higher mean scores for eye strain. Female participants in the study reported higher mean scores for both eye strain and perceived stress. Additionally, the study found significant associations between eye strain and the electronic devices used, the program of study, and perceived stress levels. The participants’ ethnicity was also found to impact eye strain levels. The study concludes that the transition to online learning during COVID-19 caused moderate to severe levels of eye strain and mental stress, indicating the need for interventions for the student community.