This paper addresses the problem of imposing pre-defined performance characteristics (by means of maximum steady-state error and minimum convergence rate) on the output tracking errors for a class of uncertain multi-input multi-output (MIMO) nonlinear system in the presence of state quantization implemented by uniform-hysteretic quantizers. A low-complexity control design that requires reduced system knowledge and utilizes only quantized measurements of the state is proposed. The desired performance is achieved by assuming knowledge of the step-size of the quantizers involved. Simulation results verify the theoretical findings.