Fluctuations in the oil market can significantly influence various sectors of the economy, such as the stock markets of countries that rely heavily on oil revenues. Oil prices are one of the key influential external factors affecting the stock exchange index of oil-dependent Iran. This paper investigates the spillover effects of oil prices on Iran’s stock exchange index weekly from March 2009 to March 2020. Using a time-series wavelet decomposition approach, a series of OPEC oil prices and Iran’s total stock market index were decomposed into various time scales (4 levels) to analyze oil market spillover into the stock market using the multivariate GARCH TBEKK model. The results confirmed that volatility spillover from the oil to the stock market occurred in all the time scales (short, medium, and long term). However, the spillover in the long term is more pronounced than over the short, demonstrating that stock market volatility is strongly influenced by long-term exogenous oil price fluctuations. Hence, oil market shocks are one of the influential factors affecting stock market turbulence in Iran.