This study aims to examine the time-varying efficiency of the Turkish stock market’s major stock index and eight sectoral indices, including the industrial, financial, service, information technology, basic metals, tourism, real estate investment, and chemical petrol plastic, during the COVID-19 outbreak and the global financial crisis (GFC) within the framework of the adaptive market hypothesis. This study employs multifractal detrended fluctuation analysis to illustrate these sectors’ multifractality and short- and long-term dependence. The results show that all sectoral returns have greater persistence during the COVID-19 outbreak than during the GFC. Second, the real estate and information technology industries had the lowest levels of efficiency during the GFC and the COVID-19 outbreak. Lastly, the fat-tailed distribution has a greater effect on multifractality in these industries. Our results validate the conclusions of the adaptive market hypothesis, according to which arbitrage opportunities vary over time, and contribute to policy formulation for future outbreak-induced economic crises.