Control and stabilisation of a class of discrete-time output-dependent nonlinear stochastic system subject to missing measurements is tackled in this article. First, a Bernoulli-distributed white sequence satisfying a known conditional probability distribution is introduced into the output measurement equation to describe the missing measurement phenomenon. Then, an observer-based controller is designed by employing the backstepping technique and the stability of the resulting closed-loop system is investigated by utilising the Lyapunov stability theory. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed control scheme.