There is currently little available evidence about the causal relationship between HIV infection and Coronavirus disease 2019 (COVID-19), and these relationships may differ across populations and socioeconomic contexts. In this study, two-sample Mendelian randomisation analyses were conducted using summary-level data from genome-wide association studies of the European ancestry population. We initially examined the causality from HIV-1 infection to the spectrum of COVID-19 [severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection, COVID-19 hospitalisation, and very severe respiratory disease]. Then we additionally tested the causality from socioeconomic-position (SEP) indicators (educational attainment and household income) to HIV-1 infection, and from educational attainment and household income to the spectrum of COVID-19. We also tested the causality from HIV-1 infection to body height as a negative control. Null causality from HIV-1 infection to the spectrum of COVID-19 was found. The risk of HIV-1 infection significantly decreased as educational attainment and household income increased. Higher educational attainment was causally associated with lower odds of the spectrum of COVID-19. Higher household income was causally associated with lower odds of COVID-19 hospitalisation and very severe respiratory disease. Negative control shared a similar result with the estimates between HIV-1 infection and the spectrum of COVID-19. We concluded that HIV-1 infection was not causally associated with SARS-CoV-2 infection, COVID-19 hospitalisation, and very severe respiratory disease. Reduction in socioeconomic inequality could potentially ameliorate COVID-19-related and HIV-related health inequities.