This paper used the Markov-switching (MS)-based wavelet analysis technique to study the dependence structure and the time–frequency impact of exchange rates on crude oil prices (West Texas Intermediate (WTI)) and stock returns. Daily data from 1 January 2005 to 1 March 2020 were collected for exchange rates, crude oil prices, and the BRICS stock market returns. The findings indicate that crude oil prices display higher volatility compared to stock returns and exchange rates. Furthermore, the wavelet analysis reveals consistent changes in the co-movement patterns of both volatility regimes, albeit with some variations in the time periods and frequency domains. The time–frequency dependence between Brazilian, Indian, and Chinese stock markets and crude oil is significantly influenced by exchange rates, which play a pivotal role in their co-movement in the medium term. The findings reveal that these three countries share economic interests, have strong economic ties and interdependencies, and may be motivated to cooperate during crisis periods. However, when it comes to Russia and South Africa (SA), exchange rates do not exhibit a long-term impact on the co-movement in time–frequency. Therefore, we recommend investors to look for investment opportunities that are less correlated with the co-moving markets.