The time-varying correlation between oil prices returns and European industrial sector indices returns, considering the origin of the oil price shock, is investigated. A time-varying multivariate heteroskedastic framework is employed to test the above hypothesis based on data from 10 European sectors. The contemporaneous correlations suggest that the relationship between sector indices and oil prices change over time and they are industry specific. In addition, the supply-side oil price shocks result in low to moderate positive correlation levels, the precautionary demand oil price shocks lead to almost zero correlation levels, whereas the aggregate demand oil price shocks generate significant changes in the correlation levels (either positive or negative). Both the origin of the oil price shock and the type of industry are important determinants of the correlation level between industrial sectors’ returns and oil prices. Prominent among the results is the fact that during the financial crisis of 2008 some sectors were providing diversification opportunities to investors dealing with the crude oil market.