Sustainable investment is widely regarded as an important market-based approach to achieving inclusive green growth. To achieve the inclusive green growth objective, companies providing sustainable products must be profitable enough to attract private capital. Oil price changes can however affect the profitability of such companies. This study assesses volatility transmission between crude oil prices and sustainable investment in the USA. Using the dynamic conditional correlation-generalized autoregressive conditional heteroskedasticity (DCC-GARCH) method, daily data from September 28, 2012, to October 19, 2022, is analyzed. There are several key findings from this analysis. The risk connectedness of crude oil and sustainable investment is found to vary with time. Results further show that the risk connectedness increases in periods of important economic and geopolitical events. The greatest risk connectedness of crude oil and sustainable investment is observed during the outbreak of coronavirus disease (COVID-19). Moreover, the result shows that crude oil is the main risk transmitter, whereas, both the energy efficiency and pollution mitigation indices (i.e., sustainable investment) are risk receivers, and crude oil is constantly dominating sustainable investment. The study findings provide valuable insights for investors and policymakers alike.