Based on the dual theoretical framework of the Knowledge-Attitude-Practice (KAP) theory and the Rainbow Model, this study systematically analyzes the key factors influencing the development of science popularization competencies among medical students using a dual analytical framework of "internal and external factors". Data were collected from 699 valid questionnaires administered at a medical university. Linear regression models were employed to assess the association between science popularization competency (dependent variable) and variables derived from the dual framework (independent variables: intrinsic and extrinsic factors). The Shapley value decomposition method was used to estimate the relative contributions of each variable to model fit. Internal factors, including knowledge (β = 2.758, 95% CI: 2.472–3.044), attitude (β = 0.950, 95% CI: 0.647–1.254), and practice (β = 0.531, 95% CI: 0.232–0.829), significantly promoted science popularization competency. Among external factors, institutional-level influences also demonstrated a positive effect (β = 0.714, 95% CI: 0.285–1.142). Shapley decomposition revealed that knowledge and attitude contributed most substantially to the model. Knowledge, attitude, and practice serve as core drivers of science popularization competency in medical students, while institutional factors act as critical auxiliary elements. Among internal drivers, knowledge and attitude exhibit the highest explanatory power. The findings suggest that medical universities should prioritize both knowledge instruction and attitude guidance, while strengthening external support for health science popularization policies. This will effectively enhance the science popularization competencies of medical students and lay a solid foundation for improving public health literacy.