This article provides an empirical investigation of the time-varying dependence between oil prices and stock markets in the top ten net oil-exporting countries. Using daily data focusing on COVID-19 period, we implement the DCCGARCH to identify the dynamic dependence. Then, we apply structural break techniques to detect the shift in the dependence structure. We find that there exists a positive time-varying dependence between oil returns and stock returns during the ongoing COVID-19 pandemic wherein the breakpoints mostly coincided with the emergence of oil price war and global stock market crash. Overall, results imply that declining oil prices lead to a fall in stock returns due to lower future earnings for oil companies, exhibiting a signal of reduction in aggregate demand and economic activity in oil-exporting countries. Thus, the high positive co-movement may have ill-effects on portfolio diversification, as the latter will be less effective if the asset returns are highly correlated.