The purpose of this paper is to determine whether there was information flow between the stock markets of Zimbabwe and South Africa during the time the Zimbabwean economy was dollarized. The author used econophysics-based Shannonian and Rényian transfer entropy estimates to establish the flow of information between the markets in tranquil periods as well as at the tails of return distributions. The only significant Shannonian transfer entropy estimate was from Johannesburg Stock Exchange (JSE) resources index to Zimbabwe Stock Exchange (ZSE) mining index. The findings show that the only significant tail dependence was between JSE All Share Index (JALSH) and ZSE Mining on the one hand, and between JSE Resources and ZSE Mining on the other hand. However, the magnitudes of the effective transfer entropy values are relatively low, showing that there are weak linkages between the Zimbabwe Stock Exchange and the Johannesburg Stock Exchange. The lack of significant information flows between the exchanges of the two countries offer opportunities to fund managers for portfolio diversification. From a government point of view, it is imperative that the tempo of economic and political reform be accelerated so that integration between the markets can be fast-tracked. Integrated markets will benefit Zimbabwe as this will reduce the cost of equity and accelerate economic growth.