This paper analyzes the sectoral transmission structure of inflation in Korea using monthly data from January 2001 to September 2025. We estimate a Bayesian VAR model with 14 variables, including crude oil prices, CPI components, the exchange rate, real activity, and the call rate, and apply the Diebold--Yilmaz connectedness framework to assess how price shocks originating in specific sectors are transmitted to others. The empirical results show that crude oil shocks exert strong spillover effects on domestic prices, with larger effects at medium and long-term horizons. Among domestic sectors, eating-out prices display relatively persistent outgoing connectedness, while personal services, agricultural/livestock/fisheries products, and other manufactured goods tend to receive sizable spillovers from other sectors. Sub-sample comparisons show that crude oil and exchange rate spillovers were more pronounced in the early 2000s, whereas eating-out prices and rent have become more important transmission channels in the recent period. These findings suggest that Korean inflation dynamics are shaped not only by aggregate price pressures but also by the origins and propagation paths of sector-specific shocks, highlighting the need for micro-level inflation monitoring based on sectoral price networks.