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(1) Background: Here, we investigate the incidence of mpox and factors associated with vaccine uptake in mainly well-treated men who have sex with men and are living with HIV (MSMWH). (2) Methods: This study included 727 MSMWH from the Copenhagen co-morbidity in HIV infection (COCOMO) study from 1 May to 31 October 2022. Mpox infection and vaccination status were obtained from the Danish Microbiology Database and The Danish Vaccination Register. Vaccination willingness was assessed through an online survey. (3) Results: At a median follow-up of 180 days, 13 (1.8%) participants had laboratory-confirmed mpox infections. Furthermore, 238 (32.7%) had received the mpox vaccine. A sexually transmitted disease (STD) in the preceding two years was associated with a higher risk of mpox infection (hazard ratio 7.1; 95% confidence interval (CI) [1.9–26.9]) and with higher odds of vaccination (adjusted odds ratio 3.1; 95% CI [2.2–4.6]). 401 (55.2%) participants responded to the survey. 228 (57.0%) reported very high vaccination willingness. The self-perceived risk of infection was associated with vaccine uptake. (4) Conclusions: The incidence of mpox was low. A prior STD was associated with both a higher risk of mpox infection and higher odds of vaccination. Despite high-risk sexual behavior and high vaccination willingness, a sizable fraction of participants had not been vaccinated.