A cross-sectional online survey was conducted in Ghana from November to December 2022. Snowball sampling was used to recruit participants via social media platforms, such as WhatsApp, LinkedIn, Telegram, and Facebook. The validated 5C scale was used to assess five psychological factors that influence vaccination behavior and intent: confidence, complacency, constraints, calculation, and collective responsibility. Results: The study drew 605 participants; their mean age was 30.0 ± 6.8; 68.1% were single; 60.8 % were males, and 51.9% were living in Greater Accra (The capital and largest city of Ghana). About 53.9% of the studied Ghanaian population did not intend to receive the MPOX vaccination. Vaccine acceptance among non-healthcare workers (non-HCWs) was significantly lower than among HCWs (41.7 vs. 55.3, p < 0.001). The determinants of vaccine acceptance were male gender (AOR = 1.48, 95% CI, 1.00–2.18, p = 0.049), urban residence (AOR = 0.63, 95% CI, 0.41–0.96, p = 0.033), refusal of coronavirus 2019 vaccine (AOR = 0.29, 95% CI, 0.16–0.52, p < 0.001), confidence in vaccination ((AOR = 2.45, 95% CI, 1.93–3.15, and p < 0.001), and collective responsibility (AOR = 1.34, 95% CI, 1.02–1.75, p = 0.034)). Conclusions: The participants in this study did not show high levels of intention to accept the MPOX vaccination. Consequently, tailoring the efforts aiming to promote MPOX vaccination is needed especially among non-HCWs through increasing their confidence in vaccine effectiveness and safety and promoting the importance of self-vaccination to protect others.