The outbreak of monkeypox across non-endemic regions confirmed in May 2022 shows epidemiological features distinct from previously imported outbreaks, most notably its observed growth and predominance amongst men who have sex with men (MSM). We use a transmission model fitted to empirical sexual partnership data to show that the heavy-tailed sexual partnership distribution, in which a handful of individuals have disproportionately many partners, can explain the sustained growth of monkeypox among MSM despite the absence of such patterns previously. We suggest that the basic reproduction number (R0) for monkeypox over the MSM sexual network may be substantially above 1, which poses challenges to outbreak containment. Ensuring support and tailored messaging to facilitate prevention and early detection among MSM with high numbers of partners is warranted.