This study examined how the relationships among the fossil fuel, clean energy stock, gold, and Bitcoin markets have changed since the COVID-19 pandemic took place for hedging the price change risks in the fossil fuel markets. We applied the Bayesian Dynamic Conditional Correlation-Multivariate GARCH (DCC-MGARCH) models using US daily data from 2 January 2019 to 26 February 2021. Our results suggest that the fossil fuel (WTI crude oil and natural gas) and financial markets (clean energy stock, gold, and Bitcoin) generally had negative relationships in 2019 before the pandemic prevailed, but they became positive for a while in mid-2020, alternating between positive (0.8) and negative values (−0.8). As it is known that negative relationships are required among assets to hedge the risk of price changes, this implies that stakeholders need to be cautious in hedging the risk across the fossil fuel and financial markets when a crisis like COVID-19 occurs. However, our study also revealed that such negative relationships only lasted for three to six months, suggesting that the effects of the pandemic were short term and that stakeholders in the fossil fuel markets could cross hedge with the financial markets in the long term.