Epstein–Barr virus (EBV) is a well-known risk factor for the development of nasopharyngeal carcinoma, Hodgkin’s lymphoma (HL), and Non-Hodgkin’s lymphoma (NHL). People with HIV infection (PWH) are at increased risk for EBV-associated malignancies such as HL and NHL. Nevertheless, there are limited data on the burden of EBV among this population group in Ethiopia. Hence, this study aimed to determine the burden of EBV infection among adult HIV-positive individuals in Ethiopia and assess the determinants of EBV DNA positivity. We conducted a cross-sectional study at the Tikur Anbessa Specialised Hospital from March 2020 to March 2021. Two hundred and sixty individuals were enrolled in this study, including 179 HIV-positive and 81 HIV-negative individuals. A structured questionnaire was used to capture demographic and individual attributes. In addition, the clinical data of patients were also retrieved from clinical records. EBV viral capsid antigen (VCA) IgG antibody was measured by multiplex flow immunoassay, and EBV DNA levels were tested by quantitative real-time polymerase chain reaction (q-PCR) assays targeting the EBNA-1 open reading frame (ORF). Descriptive statistics were conducted to assess each study variable. A multivariable logistic regression model was applied to evaluate the determinants of EBV infection. Statistical significance was determined at a p-value < 0.05. Two hundred and fifty-three (97.7%) study participants were seropositive for the EBV VCA IgG antibody. Disaggregated by HIV status, 99.4% of HIV-positive and 93.8% of HIV-negative participants were EBV seropositive. In this study, 49.7% of HIV-positive and 24.7% of HIV-negative individuals were EBV DNA positive. PWH had a higher risk of EBV DNA positivity at 3.05 times (AOR: 3.05, 95% CI: 1.40–6.67). Moreover, among PWH, those with an HIV viral load greater than 1000 RNA copies/mL (AOR = 5.81, 95% CI = 1.40, 24.13) had a higher likelihood of EBV DNA positivity. The prevalence of EBV among PWH was significantly higher than among HIV-negative individuals. Higher HIV viral loads in PWH were associated with an increased risk of EBV DNA positivity. Since the increases in the viral load of EBV DNA among PWH could be related to the risk of developing EBV-associated cancers, it is necessary for more research on the role of EBV in EBV-associated cancer in this population group to be carried out.