In 2015, Botswana introduced the quadrivalent human papillomavirus (HPV) vaccine as a two-dose schedule in girls aged 9–13 years. We sought to establish a baseline HPV prevalence in unvaccinated young adults in Botswana. HIV-uninfected men and women aged 18–22 years were recruited from the University of Botswana in Gaborone during October 2019–February 2021. Demographic and behavioural characteristics were self-reported during structured interviews. Self-collected vaginal and penile swabs were tested for 28 HPV types using Seegene Anyplex II HPV28. We compared any HPV type, quadrivalent vaccine (HPV 6, 11, 16, 18)-type and non-quadrivalent vaccine-type prevalence in men and women and evaluated the risk factors for prevalence of any HPV type. A total of 493 men and 500 women were included in the analysis. Compared to men, women had higher prevalence of any HPV type (63.0% versus 31.4%, P < 0.001), vaccine-type HPV (21% versus 9.7%, P < 0.001) and non-vaccine-type HPV (60.4% versus 28.4%, P < 0.001). Higher prevalence of any HPV type in men and women was associated with having ≥2 sex partners in the past 12 months; always using condoms in the past 3 months was associated with a lower HPV prevalence. These data provide baseline information for future evaluation of the population impact of the HPV vaccination programme, including potential herd effects in men.