We construct daily realized volatility, skewness, and kurtosis using 5-min data of eight Chinese commodity futures and the Chinese stock market index from March 26, 2018 to October 22, 2020, then analyse the dynamic spillovers of realized moments among these markets. The results show that the spillover effects between commodity and stock markets intensify during shock periods such as ‘trade disputes between China and the United States’ and ‘COVID-19’. Volatility spillovers are relatively stronger than spillovers in skewness or spillovers in kurtosis; however, spillovers in higher-order moments seem to contain additional information. Shocks from the silver market influence realized moments of other markets. Soybean, corn, aluminium, and oil markets are affected by other markets. The contribution of wheat as a net transmitter to the system of spillovers between stock and commodity markets is only observed at higher-order realized moments. The results from OLS and quantile regressions show that the total spillovers are generally affected by the US stock market, economic uncertainties, and the COVID-19 outbreak.