We consider stochastic zero-sum differential games (SZSDGs) described by fully-coupled forward-backward stochastic differential equations (FBSDEs). The fully-coupled FBSDE means that the drift and diffusion terms of forward SDEs depend on the solution of the backward SDE (BSDE). The objective functional is modeled by the BSDE part of the FBSDE. For the lower and upper value functions of the SZSDG, we establish the dynamic programming principle via the generalized stochastic backward semigroup associated with the BSDE. We then show that the (lower and upper) value functions are viscosity solutions to the associated HamiltonJacobi-Isaacs partial differential equations together with an algebraic equation. This additional algebraic equation emerges due to dependence of the diffusion term on the solution of the BSDE. The problem formulation and the results of this paper generalize those in the existing literature on SZSDGs to the controlled FBSDE framework.