Background The outbreak of Mpox in China has rendered the promotion of effective preventive measures among susceptible populations particularly crucial. We aimed to explore the correlates and develop a model for Mpox vaccination intention. Methods We distributed a questionnaire to a sample of 2403 men who have sex with men to investigate whether they would get a Mpox vaccine. The participants were randomly split into a training set and a testing set in a ratio of 3:1. We screened relevant variables by the least absolute shrinkage and selection operator (LASSO) regression analysis and included them into a Mpox vaccination intention model, which used a multivariate logistic regression analysis and presented the findings as a nomogram. We used the receiver operating characteristic curve, calibration curve, Kolmogorov-Smirnov test, lift test, and population stability index to test the validity and stability of the model. Results Of the 2403 participants in our sample, 87.1% intended to get an Mpox vaccine. Five of the thirty-one screened variables, i.e. Mpox knowledge, social support, vaccination internal rewards, vaccination external rewards, and vaccination response efficacy, were included in the vaccination intention model. The model demonstrated strong risk differentiation (Kolmogorov-Smirnov value = 0.46), moderate predictive power (training area under the curve = 0.7709), and good calibration fit, indicating robust performance. Conclusions Our proposed model has a good performance and is highly stable, while our findings suggest that governments should design targeted public health strategies, integrating social engagement and leveraging peer and community education to promote Mpox vaccination.