Introduction: This study was planned to understand the continuity of the follow-up and treatment of people newly diagnosed with HIV infection during the COVID-19 pandemic. We compared the pre-pandemic to the pandemic period, focusing on factors such as diagnosis, accessing treatment, staying on treatment, and viral suppression, as the pandemic had the potential to disrupt HIV care. Methodology: The one-year follow-up data of patients diagnosed in 2018 (pre-pandemic era) and 2020 (pandemic era) were compared. Each patient’s age, gender, employment and educational status, sexual orientation, comorbidities, quantitative HIV RNA levels (qRT-PCR), and CD4+ cell counts during outpatient follow-up visits, regular use of the treatment, and regular visits to the outpatient clinic were investigated retrospectively. Results: We had 192 new patients during the pre-pandemic period in 2018 (Group A) and 118 new patients during the pandemic in 2020 (Group B). There was no difference between the two groups regarding patient age and gender. The number of newly diagnosed HIV patients during the pandemic period decreased compared to the previous period (p < 0.001). Compliance with treatment rates was similar in both periods. There was no statistical difference in HIV RNA between the two groups after one year of treatment. Conclusions: The COVID-19 pandemic has had the potential to disrupt the continuity of HIV care among individuals. Although the COVID pandemic had a statistically significant effect on attendance at HIV care programs, treatment compliance was not impaired due to rapid action on drug supply and correct policy implementation during the pandemic.